## size 27
QUANDLES[27] := rec( total := -1, implemented := 65, size := 27, rack := [ ] );
QUANDLES[27].implemented := 1;
QUANDLES[27].rack[1] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 5, 4, 6, 9, 8, 7, 19, 21, 20, 23, 22, 24, 27, 26, 25, 10, 12, 11, 14, 13, 15, 18, 17, 16 ], 
  [ 3, 2, 1, 4, 6, 5, 8, 7, 9, 25, 27, 26, 20, 19, 21, 24, 23, 22, 14, 13, 15, 18, 17, 16, 10, 12, 11 ], 
  [ 2, 1, 3, 6, 5, 4, 7, 9, 8, 22, 24, 23, 26, 25, 27, 21, 20, 19, 18, 17, 16, 10, 12, 11, 14, 13, 15 ], 
  [ 3, 2, 1, 4, 6, 5, 8, 7, 9, 25, 27, 26, 20, 19, 21, 24, 23, 22, 14, 13, 15, 18, 17, 16, 10, 12, 11 ], 
  [ 2, 1, 3, 6, 5, 4, 7, 9, 8, 22, 24, 23, 26, 25, 27, 21, 20, 19, 18, 17, 16, 10, 12, 11, 14, 13, 15 ], 
  [ 1, 3, 2, 5, 4, 6, 9, 8, 7, 19, 21, 20, 23, 22, 24, 27, 26, 25, 10, 12, 11, 14, 13, 15, 18, 17, 16 ], 
  [ 2, 1, 3, 6, 5, 4, 7, 9, 8, 22, 24, 23, 26, 25, 27, 21, 20, 19, 18, 17, 16, 10, 12, 11, 14, 13, 15 ], 
  [ 1, 3, 2, 5, 4, 6, 9, 8, 7, 19, 21, 20, 23, 22, 24, 27, 26, 25, 10, 12, 11, 14, 13, 15, 18, 17, 16 ], 
  [ 3, 2, 1, 4, 6, 5, 8, 7, 9, 25, 27, 26, 20, 19, 21, 24, 23, 22, 14, 13, 15, 18, 17, 16, 10, 12, 11 ], 
  [ 19, 21, 20, 23, 22, 24, 27, 26, 25, 10, 12, 11, 14, 13, 15, 18, 17, 16, 1, 3, 2, 5, 4, 6, 9, 8, 7 ], 
  [ 23, 22, 24, 27, 26, 25, 19, 21, 20, 12, 11, 10, 13, 15, 14, 17, 16, 18, 7, 9, 8, 2, 1, 3, 6, 5, 4 ], 
  [ 27, 26, 25, 19, 21, 20, 23, 22, 24, 11, 10, 12, 15, 14, 13, 16, 18, 17, 4, 6, 5, 8, 7, 9, 3, 2, 1 ], 
  [ 23, 22, 24, 27, 26, 25, 19, 21, 20, 12, 11, 10, 13, 15, 14, 17, 16, 18, 7, 9, 8, 2, 1, 3, 6, 5, 4 ], 
  [ 27, 26, 25, 19, 21, 20, 23, 22, 24, 11, 10, 12, 15, 14, 13, 16, 18, 17, 4, 6, 5, 8, 7, 9, 3, 2, 1 ], 
  [ 19, 21, 20, 23, 22, 24, 27, 26, 25, 10, 12, 11, 14, 13, 15, 18, 17, 16, 1, 3, 2, 5, 4, 6, 9, 8, 7 ], 
  [ 27, 26, 25, 19, 21, 20, 23, 22, 24, 11, 10, 12, 15, 14, 13, 16, 18, 17, 4, 6, 5, 8, 7, 9, 3, 2, 1 ], 
  [ 19, 21, 20, 23, 22, 24, 27, 26, 25, 10, 12, 11, 14, 13, 15, 18, 17, 16, 1, 3, 2, 5, 4, 6, 9, 8, 7 ], 
  [ 23, 22, 24, 27, 26, 25, 19, 21, 20, 12, 11, 10, 13, 15, 14, 17, 16, 18, 7, 9, 8, 2, 1, 3, 6, 5, 4 ], 
  [ 10, 12, 11, 14, 13, 15, 18, 17, 16, 1, 3, 2, 5, 4, 6, 9, 8, 7, 19, 21, 20, 23, 22, 24, 27, 26, 25 ], 
  [ 16, 18, 17, 11, 10, 12, 15, 14, 13, 5, 4, 6, 9, 8, 7, 1, 3, 2, 21, 20, 19, 22, 24, 23, 26, 25, 27 ], 
  [ 13, 15, 14, 17, 16, 18, 12, 11, 10, 9, 8, 7, 1, 3, 2, 5, 4, 6, 20, 19, 21, 24, 23, 22, 25, 27, 26 ], 
  [ 16, 18, 17, 11, 10, 12, 15, 14, 13, 5, 4, 6, 9, 8, 7, 1, 3, 2, 21, 20, 19, 22, 24, 23, 26, 25, 27 ], 
  [ 13, 15, 14, 17, 16, 18, 12, 11, 10, 9, 8, 7, 1, 3, 2, 5, 4, 6, 20, 19, 21, 24, 23, 22, 25, 27, 26 ], 
  [ 10, 12, 11, 14, 13, 15, 18, 17, 16, 1, 3, 2, 5, 4, 6, 9, 8, 7, 19, 21, 20, 23, 22, 24, 27, 26, 25 ], 
  [ 13, 15, 14, 17, 16, 18, 12, 11, 10, 9, 8, 7, 1, 3, 2, 5, 4, 6, 20, 19, 21, 24, 23, 22, 25, 27, 26 ], 
  [ 10, 12, 11, 14, 13, 15, 18, 17, 16, 1, 3, 2, 5, 4, 6, 9, 8, 7, 19, 21, 20, 23, 22, 24, 27, 26, 25 ], 
  [ 16, 18, 17, 11, 10, 12, 15, 14, 13, 5, 4, 6, 9, 8, 7, 1, 3, 2, 21, 20, 19, 22, 24, 23, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 2;
QUANDLES[27].rack[2] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 3;
QUANDLES[27].rack[3] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 22, 24, 23, 19, 21, 20, 27, 26, 25, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 26, 25, 27, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 23, 22, 24, 20, 19, 21, 25, 27, 26, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 20, 19, 21, 25, 27, 26, 22, 24, 23, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 19, 21, 20, 27, 26, 25, 24, 23, 22, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 21, 20, 19, 26, 25, 27, 23, 22, 24, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 10, 12, 11, 18, 17, 16, 15, 14, 13, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 12, 11, 10, 17, 16, 18, 14, 13, 15, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 11, 10, 12, 16, 18, 17, 13, 15, 14, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 14, 13, 15, 11, 10, 12, 16, 18, 17, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 13, 15, 14, 10, 12, 11, 18, 17, 16, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 15, 14, 13, 12, 11, 10, 17, 16, 18, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 4, 6, 5, 1, 3, 2, 9, 8, 7, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 6, 5, 4, 3, 2, 1, 8, 7, 9, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 5, 4, 6, 2, 1, 3, 7, 9, 8, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 2, 1, 3, 7, 9, 8, 4, 6, 5, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 1, 3, 2, 9, 8, 7, 6, 5, 4, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 3, 2, 1, 8, 7, 9, 5, 4, 6, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 4;
QUANDLES[27].rack[4] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 20, 19, 21, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 5;
QUANDLES[27].rack[5] := rec( size := 27, matrix :=
[ [ 1, 7, 4, 2, 8, 5, 3, 9, 6, 23, 20, 26, 24, 21, 27, 22, 19, 25, 18, 15, 12, 16, 13, 10, 17, 14, 11 ], 
  [ 5, 2, 8, 6, 3, 9, 4, 1, 7, 27, 24, 21, 25, 22, 19, 26, 23, 20, 10, 16, 13, 11, 17, 14, 12, 18, 15 ], 
  [ 9, 6, 3, 7, 4, 1, 8, 5, 2, 19, 25, 22, 20, 26, 23, 21, 27, 24, 14, 11, 17, 15, 12, 18, 13, 10, 16 ], 
  [ 6, 3, 9, 4, 1, 7, 5, 2, 8, 25, 22, 19, 26, 23, 20, 27, 24, 21, 11, 17, 14, 12, 18, 15, 10, 16, 13 ], 
  [ 7, 4, 1, 8, 5, 2, 9, 6, 3, 20, 26, 23, 21, 27, 24, 19, 25, 22, 15, 12, 18, 13, 10, 16, 14, 11, 17 ], 
  [ 2, 8, 5, 3, 9, 6, 1, 7, 4, 24, 21, 27, 22, 19, 25, 23, 20, 26, 16, 13, 10, 17, 14, 11, 18, 15, 12 ], 
  [ 8, 5, 2, 9, 6, 3, 7, 4, 1, 21, 27, 24, 19, 25, 22, 20, 26, 23, 13, 10, 16, 14, 11, 17, 15, 12, 18 ], 
  [ 3, 9, 6, 1, 7, 4, 2, 8, 5, 22, 19, 25, 23, 20, 26, 24, 21, 27, 17, 14, 11, 18, 15, 12, 16, 13, 10 ], 
  [ 4, 1, 7, 5, 2, 8, 6, 3, 9, 26, 23, 20, 27, 24, 21, 25, 22, 19, 12, 18, 15, 10, 16, 13, 11, 17, 14 ], 
  [ 27, 24, 21, 25, 22, 19, 26, 23, 20, 10, 16, 13, 11, 17, 14, 12, 18, 15, 5, 2, 8, 6, 3, 9, 4, 1, 7 ], 
  [ 19, 25, 22, 20, 26, 23, 21, 27, 24, 14, 11, 17, 15, 12, 18, 13, 10, 16, 9, 6, 3, 7, 4, 1, 8, 5, 2 ], 
  [ 23, 20, 26, 24, 21, 27, 22, 19, 25, 18, 15, 12, 16, 13, 10, 17, 14, 11, 1, 7, 4, 2, 8, 5, 3, 9, 6 ], 
  [ 20, 26, 23, 21, 27, 24, 19, 25, 22, 15, 12, 18, 13, 10, 16, 14, 11, 17, 7, 4, 1, 8, 5, 2, 9, 6, 3 ], 
  [ 24, 21, 27, 22, 19, 25, 23, 20, 26, 16, 13, 10, 17, 14, 11, 18, 15, 12, 2, 8, 5, 3, 9, 6, 1, 7, 4 ], 
  [ 25, 22, 19, 26, 23, 20, 27, 24, 21, 11, 17, 14, 12, 18, 15, 10, 16, 13, 6, 3, 9, 4, 1, 7, 5, 2, 8 ], 
  [ 22, 19, 25, 23, 20, 26, 24, 21, 27, 17, 14, 11, 18, 15, 12, 16, 13, 10, 3, 9, 6, 1, 7, 4, 2, 8, 5 ], 
  [ 26, 23, 20, 27, 24, 21, 25, 22, 19, 12, 18, 15, 10, 16, 13, 11, 17, 14, 4, 1, 7, 5, 2, 8, 6, 3, 9 ], 
  [ 21, 27, 24, 19, 25, 22, 20, 26, 23, 13, 10, 16, 14, 11, 17, 15, 12, 18, 8, 5, 2, 9, 6, 3, 7, 4, 1 ], 
  [ 14, 11, 17, 15, 12, 18, 13, 10, 16, 9, 6, 3, 7, 4, 1, 8, 5, 2, 19, 25, 22, 20, 26, 23, 21, 27, 24 ], 
  [ 18, 15, 12, 16, 13, 10, 17, 14, 11, 1, 7, 4, 2, 8, 5, 3, 9, 6, 23, 20, 26, 24, 21, 27, 22, 19, 25 ], 
  [ 10, 16, 13, 11, 17, 14, 12, 18, 15, 5, 2, 8, 6, 3, 9, 4, 1, 7, 27, 24, 21, 25, 22, 19, 26, 23, 20 ], 
  [ 16, 13, 10, 17, 14, 11, 18, 15, 12, 2, 8, 5, 3, 9, 6, 1, 7, 4, 24, 21, 27, 22, 19, 25, 23, 20, 26 ], 
  [ 11, 17, 14, 12, 18, 15, 10, 16, 13, 6, 3, 9, 4, 1, 7, 5, 2, 8, 25, 22, 19, 26, 23, 20, 27, 24, 21 ], 
  [ 15, 12, 18, 13, 10, 16, 14, 11, 17, 7, 4, 1, 8, 5, 2, 9, 6, 3, 20, 26, 23, 21, 27, 24, 19, 25, 22 ], 
  [ 12, 18, 15, 10, 16, 13, 11, 17, 14, 4, 1, 7, 5, 2, 8, 6, 3, 9, 26, 23, 20, 27, 24, 21, 25, 22, 19 ], 
  [ 13, 10, 16, 14, 11, 17, 15, 12, 18, 8, 5, 2, 9, 6, 3, 7, 4, 1, 21, 27, 24, 19, 25, 22, 20, 26, 23 ], 
  [ 17, 14, 11, 18, 15, 12, 16, 13, 10, 3, 9, 6, 1, 7, 4, 2, 8, 5, 22, 19, 25, 23, 20, 26, 24, 21, 27 ] ]);
QUANDLES[27].implemented := 6;
QUANDLES[27].rack[6] := rec( size := 27, matrix :=
[ [ 1, 2, 3, 21, 19, 20, 11, 12, 10, 4, 5, 6, 22, 23, 24, 13, 14, 15, 7, 8, 9, 26, 27, 25, 18, 16, 17 ], 
  [ 1, 2, 3, 21, 19, 20, 11, 12, 10, 4, 5, 6, 22, 23, 24, 13, 14, 15, 7, 8, 9, 26, 27, 25, 18, 16, 17 ], 
  [ 1, 2, 3, 21, 19, 20, 11, 12, 10, 4, 5, 6, 22, 23, 24, 13, 14, 15, 7, 8, 9, 26, 27, 25, 18, 16, 17 ], 
  [ 13, 14, 15, 4, 5, 6, 22, 23, 24, 16, 17, 18, 8, 9, 7, 27, 25, 26, 10, 11, 12, 3, 1, 2, 20, 21, 19 ], 
  [ 13, 14, 15, 4, 5, 6, 22, 23, 24, 16, 17, 18, 8, 9, 7, 27, 25, 26, 10, 11, 12, 3, 1, 2, 20, 21, 19 ], 
  [ 13, 14, 15, 4, 5, 6, 22, 23, 24, 16, 17, 18, 8, 9, 7, 27, 25, 26, 10, 11, 12, 3, 1, 2, 20, 21, 19 ], 
  [ 26, 27, 25, 18, 16, 17, 7, 8, 9, 20, 21, 19, 10, 11, 12, 3, 1, 2, 23, 24, 22, 14, 15, 13, 5, 6, 4 ], 
  [ 26, 27, 25, 18, 16, 17, 7, 8, 9, 20, 21, 19, 10, 11, 12, 3, 1, 2, 23, 24, 22, 14, 15, 13, 5, 6, 4 ], 
  [ 26, 27, 25, 18, 16, 17, 7, 8, 9, 20, 21, 19, 10, 11, 12, 3, 1, 2, 23, 24, 22, 14, 15, 13, 5, 6, 4 ], 
  [ 16, 17, 18, 8, 9, 7, 27, 25, 26, 10, 11, 12, 3, 1, 2, 20, 21, 19, 13, 14, 15, 4, 5, 6, 22, 23, 24 ], 
  [ 16, 17, 18, 8, 9, 7, 27, 25, 26, 10, 11, 12, 3, 1, 2, 20, 21, 19, 13, 14, 15, 4, 5, 6, 22, 23, 24 ], 
  [ 16, 17, 18, 8, 9, 7, 27, 25, 26, 10, 11, 12, 3, 1, 2, 20, 21, 19, 13, 14, 15, 4, 5, 6, 22, 23, 24 ], 
  [ 19, 20, 21, 12, 10, 11, 2, 3, 1, 22, 23, 24, 13, 14, 15, 4, 5, 6, 25, 26, 27, 17, 18, 16, 9, 7, 8 ], 
  [ 19, 20, 21, 12, 10, 11, 2, 3, 1, 22, 23, 24, 13, 14, 15, 4, 5, 6, 25, 26, 27, 17, 18, 16, 9, 7, 8 ], 
  [ 19, 20, 21, 12, 10, 11, 2, 3, 1, 22, 23, 24, 13, 14, 15, 4, 5, 6, 25, 26, 27, 17, 18, 16, 9, 7, 8 ], 
  [ 5, 6, 4, 23, 24, 22, 14, 15, 13, 8, 9, 7, 27, 25, 26, 16, 17, 18, 2, 3, 1, 19, 20, 21, 12, 10, 11 ], 
  [ 5, 6, 4, 23, 24, 22, 14, 15, 13, 8, 9, 7, 27, 25, 26, 16, 17, 18, 2, 3, 1, 19, 20, 21, 12, 10, 11 ], 
  [ 5, 6, 4, 23, 24, 22, 14, 15, 13, 8, 9, 7, 27, 25, 26, 16, 17, 18, 2, 3, 1, 19, 20, 21, 12, 10, 11 ], 
  [ 22, 23, 24, 13, 14, 15, 4, 5, 6, 25, 26, 27, 17, 18, 16, 9, 7, 8, 19, 20, 21, 12, 10, 11, 2, 3, 1 ], 
  [ 22, 23, 24, 13, 14, 15, 4, 5, 6, 25, 26, 27, 17, 18, 16, 9, 7, 8, 19, 20, 21, 12, 10, 11, 2, 3, 1 ], 
  [ 22, 23, 24, 13, 14, 15, 4, 5, 6, 25, 26, 27, 17, 18, 16, 9, 7, 8, 19, 20, 21, 12, 10, 11, 2, 3, 1 ], 
  [ 7, 8, 9, 26, 27, 25, 18, 16, 17, 1, 2, 3, 21, 19, 20, 11, 12, 10, 4, 5, 6, 22, 23, 24, 13, 14, 15 ], 
  [ 7, 8, 9, 26, 27, 25, 18, 16, 17, 1, 2, 3, 21, 19, 20, 11, 12, 10, 4, 5, 6, 22, 23, 24, 13, 14, 15 ], 
  [ 7, 8, 9, 26, 27, 25, 18, 16, 17, 1, 2, 3, 21, 19, 20, 11, 12, 10, 4, 5, 6, 22, 23, 24, 13, 14, 15 ], 
  [ 11, 12, 10, 1, 2, 3, 21, 19, 20, 14, 15, 13, 5, 6, 4, 23, 24, 22, 17, 18, 16, 9, 7, 8, 25, 26, 27 ], 
  [ 11, 12, 10, 1, 2, 3, 21, 19, 20, 14, 15, 13, 5, 6, 4, 23, 24, 22, 17, 18, 16, 9, 7, 8, 25, 26, 27 ], 
  [ 11, 12, 10, 1, 2, 3, 21, 19, 20, 14, 15, 13, 5, 6, 4, 23, 24, 22, 17, 18, 16, 9, 7, 8, 25, 26, 27 ] ]);
QUANDLES[27].implemented := 7;
QUANDLES[27].rack[7] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 2, 1, 3, 25, 27, 26, 24, 23, 22, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 8, 7, 9, 6, 5, 4, 1, 3, 2, 27, 26, 25, 23, 22, 24, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 7, 9, 8, 5, 4, 6, 3, 2, 1, 26, 25, 27, 22, 24, 23, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 23, 22, 24, 21, 20, 19, 25, 27, 26, 15, 14, 13, 10, 12, 11, 17, 16, 18 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 22, 24, 23, 20, 19, 21, 27, 26, 25, 14, 13, 15, 12, 11, 10, 16, 18, 17 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 24, 23, 22, 19, 21, 20, 26, 25, 27, 13, 15, 14, 11, 10, 12, 18, 17, 16 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 10, 12, 11, 17, 16, 18, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 12, 11, 10, 16, 18, 17, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 11, 10, 12, 18, 17, 16, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 13, 15, 14, 11, 10, 12, 8, 7, 9, 4, 6, 5, 3, 2, 1 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 15, 14, 13, 10, 12, 11, 7, 9, 8, 6, 5, 4, 2, 1, 3 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 14, 13, 15, 12, 11, 10, 9, 8, 7, 5, 4, 6, 1, 3, 2 ], 
  [ 22, 24, 23, 20, 19, 21, 27, 26, 25, 14, 13, 15, 12, 11, 10, 16, 18, 17, 6, 5, 4, 1, 3, 2, 8, 7, 9 ], 
  [ 24, 23, 22, 19, 21, 20, 26, 25, 27, 13, 15, 14, 11, 10, 12, 18, 17, 16, 5, 4, 6, 3, 2, 1, 7, 9, 8 ], 
  [ 23, 22, 24, 21, 20, 19, 25, 27, 26, 15, 14, 13, 10, 12, 11, 17, 16, 18, 4, 6, 5, 2, 1, 3, 9, 8, 7 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 7, 9, 8, 6, 5, 4, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 9, 8, 7, 5, 4, 6, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 8, 7, 9, 4, 6, 5, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 18, 17, 16, 14, 13, 15, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 22, 24, 23, 20, 19, 21 ], 
  [ 17, 16, 18, 13, 15, 14, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 24, 23, 22, 19, 21, 20 ], 
  [ 16, 18, 17, 15, 14, 13, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 23, 22, 24, 21, 20, 19 ], 
  [ 13, 15, 14, 11, 10, 12, 18, 17, 16, 5, 4, 6, 3, 2, 1, 7, 9, 8, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 15, 14, 13, 10, 12, 11, 17, 16, 18, 4, 6, 5, 2, 1, 3, 9, 8, 7, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 14, 13, 15, 12, 11, 10, 16, 18, 17, 6, 5, 4, 1, 3, 2, 8, 7, 9, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 8;
QUANDLES[27].rack[8] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 21, 20, 27, 26, 25, 23, 22, 24, 10, 12, 11, 17, 16, 18, 15, 14, 13 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 26, 25, 27, 22, 24, 23, 12, 11, 10, 16, 18, 17, 14, 13, 15 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 20, 19, 21, 25, 27, 26, 24, 23, 22, 11, 10, 12, 18, 17, 16, 13, 15, 14 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 23, 22, 24, 21, 20, 19, 18, 17, 16, 14, 13, 15, 10, 12, 11 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 22, 24, 23, 20, 19, 21, 17, 16, 18, 13, 15, 14, 12, 11, 10 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 24, 23, 22, 19, 21, 20, 16, 18, 17, 15, 14, 13, 11, 10, 12 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 20, 19, 21, 27, 26, 25, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 7, 9, 8, 6, 5, 4 ], 
  [ 19, 21, 20, 26, 25, 27, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 9, 8, 7, 5, 4, 6 ], 
  [ 21, 20, 19, 25, 27, 26, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 8, 7, 9, 4, 6, 5 ], 
  [ 25, 27, 26, 24, 23, 22, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 6, 5, 4, 1, 3, 2 ], 
  [ 27, 26, 25, 23, 22, 24, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 5, 4, 6, 3, 2, 1 ], 
  [ 26, 25, 27, 22, 24, 23, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 4, 6, 5, 2, 1, 3 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 12, 11, 10, 17, 16, 18, 13, 15, 14, 3, 2, 1, 7, 9, 8, 5, 4, 6, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 11, 10, 12, 16, 18, 17, 15, 14, 13, 2, 1, 3, 9, 8, 7, 4, 6, 5, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 10, 12, 11, 18, 17, 16, 14, 13, 15, 1, 3, 2, 8, 7, 9, 6, 5, 4, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 18, 17, 16, 13, 15, 14, 11, 10, 12, 8, 7, 9, 4, 6, 5, 3, 2, 1, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 17, 16, 18, 15, 14, 13, 10, 12, 11, 7, 9, 8, 6, 5, 4, 2, 1, 3, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 16, 18, 17, 14, 13, 15, 12, 11, 10, 9, 8, 7, 5, 4, 6, 1, 3, 2, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 9;
QUANDLES[27].rack[9] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 4, 6, 5, 20, 19, 21, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 14, 13, 15 ], 
  [ 3, 2, 1, 8, 7, 9, 6, 5, 4, 19, 21, 20, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 13, 15, 14 ], 
  [ 2, 1, 3, 7, 9, 8, 5, 4, 6, 21, 20, 19, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 15, 14, 13 ], 
  [ 8, 7, 9, 4, 6, 5, 1, 3, 2, 27, 26, 25, 24, 23, 22, 19, 21, 20, 18, 17, 16, 13, 15, 14, 12, 11, 10 ], 
  [ 7, 9, 8, 6, 5, 4, 3, 2, 1, 26, 25, 27, 23, 22, 24, 21, 20, 19, 17, 16, 18, 15, 14, 13, 11, 10, 12 ], 
  [ 9, 8, 7, 5, 4, 6, 2, 1, 3, 25, 27, 26, 22, 24, 23, 20, 19, 21, 16, 18, 17, 14, 13, 15, 10, 12, 11 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 23, 22, 24, 21, 20, 19, 25, 27, 26, 15, 14, 13, 10, 12, 11, 17, 16, 18 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 22, 24, 23, 20, 19, 21, 27, 26, 25, 14, 13, 15, 12, 11, 10, 16, 18, 17 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 24, 23, 22, 19, 21, 20, 26, 25, 27, 13, 15, 14, 11, 10, 12, 18, 17, 16 ], 
  [ 19, 21, 20, 25, 27, 26, 24, 23, 22, 10, 12, 11, 18, 17, 16, 13, 15, 14, 3, 2, 1, 7, 9, 8, 4, 6, 5 ], 
  [ 21, 20, 19, 27, 26, 25, 23, 22, 24, 12, 11, 10, 17, 16, 18, 15, 14, 13, 2, 1, 3, 9, 8, 7, 6, 5, 4 ], 
  [ 20, 19, 21, 26, 25, 27, 22, 24, 23, 11, 10, 12, 16, 18, 17, 14, 13, 15, 1, 3, 2, 8, 7, 9, 5, 4, 6 ], 
  [ 25, 27, 26, 23, 22, 24, 19, 21, 20, 17, 16, 18, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 2, 1, 3 ], 
  [ 27, 26, 25, 22, 24, 23, 21, 20, 19, 16, 18, 17, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 1, 3, 2 ], 
  [ 26, 25, 27, 24, 23, 22, 20, 19, 21, 18, 17, 16, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 3, 2, 1 ], 
  [ 22, 24, 23, 20, 19, 21, 27, 26, 25, 14, 13, 15, 12, 11, 10, 16, 18, 17, 6, 5, 4, 1, 3, 2, 8, 7, 9 ], 
  [ 24, 23, 22, 19, 21, 20, 26, 25, 27, 13, 15, 14, 11, 10, 12, 18, 17, 16, 5, 4, 6, 3, 2, 1, 7, 9, 8 ], 
  [ 23, 22, 24, 21, 20, 19, 25, 27, 26, 15, 14, 13, 10, 12, 11, 17, 16, 18, 4, 6, 5, 2, 1, 3, 9, 8, 7 ], 
  [ 10, 12, 11, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 4, 6, 5, 19, 21, 20, 27, 26, 25, 22, 24, 23 ], 
  [ 12, 11, 10, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 6, 5, 4, 21, 20, 19, 26, 25, 27, 24, 23, 22 ], 
  [ 11, 10, 12, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 5, 4, 6, 20, 19, 21, 25, 27, 26, 23, 22, 24 ], 
  [ 17, 16, 18, 14, 13, 15, 12, 11, 10, 8, 7, 9, 6, 5, 4, 2, 1, 3, 26, 25, 27, 22, 24, 23, 19, 21, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 11, 10, 12, 7, 9, 8, 5, 4, 6, 1, 3, 2, 25, 27, 26, 24, 23, 22, 21, 20, 19 ], 
  [ 18, 17, 16, 15, 14, 13, 10, 12, 11, 9, 8, 7, 4, 6, 5, 3, 2, 1, 27, 26, 25, 23, 22, 24, 20, 19, 21 ], 
  [ 13, 15, 14, 11, 10, 12, 18, 17, 16, 5, 4, 6, 3, 2, 1, 7, 9, 8, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 15, 14, 13, 10, 12, 11, 17, 16, 18, 4, 6, 5, 2, 1, 3, 9, 8, 7, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 14, 13, 15, 12, 11, 10, 16, 18, 17, 6, 5, 4, 1, 3, 2, 8, 7, 9, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 10;
QUANDLES[27].rack[10] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 5, 4, 6, 19, 21, 20, 25, 27, 26, 24, 23, 22, 10, 12, 11, 18, 17, 16, 13, 15, 14 ], 
  [ 3, 2, 1, 7, 9, 8, 4, 6, 5, 21, 20, 19, 27, 26, 25, 23, 22, 24, 12, 11, 10, 17, 16, 18, 15, 14, 13 ], 
  [ 2, 1, 3, 9, 8, 7, 6, 5, 4, 20, 19, 21, 26, 25, 27, 22, 24, 23, 11, 10, 12, 16, 18, 17, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 3, 2, 1, 27, 26, 25, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 12, 11, 10 ], 
  [ 8, 7, 9, 6, 5, 4, 2, 1, 3, 26, 25, 27, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 11, 10, 12 ], 
  [ 7, 9, 8, 5, 4, 6, 1, 3, 2, 25, 27, 26, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 10, 12, 11 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 20, 19, 21, 25, 27, 26, 23, 22, 24, 10, 12, 11, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 4, 6, 5 ], 
  [ 19, 21, 20, 27, 26, 25, 22, 24, 23, 12, 11, 10, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 6, 5, 4 ], 
  [ 21, 20, 19, 26, 25, 27, 24, 23, 22, 11, 10, 12, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 19, 21, 20, 18, 17, 16, 13, 15, 14, 12, 11, 10, 7, 9, 8, 6, 5, 4, 3, 2, 1 ], 
  [ 26, 25, 27, 23, 22, 24, 21, 20, 19, 17, 16, 18, 15, 14, 13, 11, 10, 12, 9, 8, 7, 5, 4, 6, 2, 1, 3 ], 
  [ 25, 27, 26, 22, 24, 23, 20, 19, 21, 16, 18, 17, 14, 13, 15, 10, 12, 11, 8, 7, 9, 4, 6, 5, 1, 3, 2 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 12, 11, 10, 18, 17, 16, 14, 13, 15, 3, 2, 1, 8, 7, 9, 6, 5, 4, 19, 21, 20, 26, 25, 27, 23, 22, 24 ], 
  [ 11, 10, 12, 17, 16, 18, 13, 15, 14, 2, 1, 3, 7, 9, 8, 5, 4, 6, 21, 20, 19, 25, 27, 26, 22, 24, 23 ], 
  [ 10, 12, 11, 16, 18, 17, 15, 14, 13, 1, 3, 2, 9, 8, 7, 4, 6, 5, 20, 19, 21, 27, 26, 25, 24, 23, 22 ], 
  [ 17, 16, 18, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 2, 1, 3, 27, 26, 25, 22, 24, 23, 21, 20, 19 ], 
  [ 16, 18, 17, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 1, 3, 2, 26, 25, 27, 24, 23, 22, 20, 19, 21 ], 
  [ 18, 17, 16, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 3, 2, 1, 25, 27, 26, 23, 22, 24, 19, 21, 20 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 11;
QUANDLES[27].rack[11] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 6, 5, 4, 21, 20, 19, 26, 25, 27, 24, 23, 22, 11, 10, 12, 18, 17, 16, 15, 14, 13 ], 
  [ 3, 2, 1, 9, 8, 7, 5, 4, 6, 20, 19, 21, 25, 27, 26, 23, 22, 24, 10, 12, 11, 17, 16, 18, 14, 13, 15 ], 
  [ 2, 1, 3, 8, 7, 9, 4, 6, 5, 19, 21, 20, 27, 26, 25, 22, 24, 23, 12, 11, 10, 16, 18, 17, 13, 15, 14 ], 
  [ 7, 9, 8, 4, 6, 5, 2, 1, 3, 27, 26, 25, 22, 24, 23, 21, 20, 19, 16, 18, 17, 15, 14, 13, 12, 11, 10 ], 
  [ 9, 8, 7, 6, 5, 4, 1, 3, 2, 26, 25, 27, 24, 23, 22, 20, 19, 21, 18, 17, 16, 14, 13, 15, 11, 10, 12 ], 
  [ 8, 7, 9, 5, 4, 6, 3, 2, 1, 25, 27, 26, 23, 22, 24, 19, 21, 20, 17, 16, 18, 13, 15, 14, 10, 12, 11 ], 
  [ 6, 5, 4, 2, 1, 3, 7, 9, 8, 22, 24, 23, 21, 20, 19, 26, 25, 27, 15, 14, 13, 11, 10, 12, 16, 18, 17 ], 
  [ 5, 4, 6, 1, 3, 2, 9, 8, 7, 24, 23, 22, 20, 19, 21, 25, 27, 26, 14, 13, 15, 10, 12, 11, 18, 17, 16 ], 
  [ 4, 6, 5, 3, 2, 1, 8, 7, 9, 23, 22, 24, 19, 21, 20, 27, 26, 25, 13, 15, 14, 12, 11, 10, 17, 16, 18 ], 
  [ 21, 20, 19, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 15, 14, 13, 1, 3, 2, 9, 8, 7, 4, 6, 5 ], 
  [ 20, 19, 21, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 14, 13, 15, 3, 2, 1, 8, 7, 9, 6, 5, 4 ], 
  [ 19, 21, 20, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 13, 15, 14, 2, 1, 3, 7, 9, 8, 5, 4, 6 ], 
  [ 26, 25, 27, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 11, 10, 12, 7, 9, 8, 5, 4, 6, 1, 3, 2 ], 
  [ 25, 27, 26, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 10, 12, 11, 9, 8, 7, 4, 6, 5, 3, 2, 1 ], 
  [ 27, 26, 25, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 12, 11, 10, 8, 7, 9, 6, 5, 4, 2, 1, 3 ], 
  [ 22, 24, 23, 21, 20, 19, 26, 25, 27, 15, 14, 13, 11, 10, 12, 16, 18, 17, 5, 4, 6, 1, 3, 2, 9, 8, 7 ], 
  [ 24, 23, 22, 20, 19, 21, 25, 27, 26, 14, 13, 15, 10, 12, 11, 18, 17, 16, 4, 6, 5, 3, 2, 1, 8, 7, 9 ], 
  [ 23, 22, 24, 19, 21, 20, 27, 26, 25, 13, 15, 14, 12, 11, 10, 17, 16, 18, 6, 5, 4, 2, 1, 3, 7, 9, 8 ], 
  [ 11, 10, 12, 16, 18, 17, 14, 13, 15, 1, 3, 2, 8, 7, 9, 5, 4, 6, 19, 21, 20, 25, 27, 26, 24, 23, 22 ], 
  [ 10, 12, 11, 18, 17, 16, 13, 15, 14, 3, 2, 1, 7, 9, 8, 4, 6, 5, 21, 20, 19, 27, 26, 25, 23, 22, 24 ], 
  [ 12, 11, 10, 17, 16, 18, 15, 14, 13, 2, 1, 3, 9, 8, 7, 6, 5, 4, 20, 19, 21, 26, 25, 27, 22, 24, 23 ], 
  [ 17, 16, 18, 15, 14, 13, 11, 10, 12, 9, 8, 7, 5, 4, 6, 2, 1, 3, 25, 27, 26, 22, 24, 23, 20, 19, 21 ], 
  [ 16, 18, 17, 14, 13, 15, 10, 12, 11, 8, 7, 9, 4, 6, 5, 1, 3, 2, 27, 26, 25, 24, 23, 22, 19, 21, 20 ], 
  [ 18, 17, 16, 13, 15, 14, 12, 11, 10, 7, 9, 8, 6, 5, 4, 3, 2, 1, 26, 25, 27, 23, 22, 24, 21, 20, 19 ], 
  [ 15, 14, 13, 11, 10, 12, 16, 18, 17, 5, 4, 6, 1, 3, 2, 9, 8, 7, 24, 23, 22, 20, 19, 21, 25, 27, 26 ], 
  [ 14, 13, 15, 10, 12, 11, 18, 17, 16, 4, 6, 5, 3, 2, 1, 8, 7, 9, 23, 22, 24, 19, 21, 20, 27, 26, 25 ], 
  [ 13, 15, 14, 12, 11, 10, 17, 16, 18, 6, 5, 4, 2, 1, 3, 7, 9, 8, 22, 24, 23, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 12;
QUANDLES[27].rack[12] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 5, 4, 6, 21, 20, 19, 26, 25, 27, 23, 22, 24, 12, 11, 10, 16, 18, 17, 15, 14, 13 ], 
  [ 3, 2, 1, 9, 8, 7, 4, 6, 5, 20, 19, 21, 25, 27, 26, 22, 24, 23, 11, 10, 12, 18, 17, 16, 14, 13, 15 ], 
  [ 2, 1, 3, 8, 7, 9, 6, 5, 4, 19, 21, 20, 27, 26, 25, 24, 23, 22, 10, 12, 11, 17, 16, 18, 13, 15, 14 ], 
  [ 8, 7, 9, 4, 6, 5, 1, 3, 2, 27, 26, 25, 24, 23, 22, 19, 21, 20, 17, 16, 18, 15, 14, 13, 11, 10, 12 ], 
  [ 7, 9, 8, 6, 5, 4, 3, 2, 1, 26, 25, 27, 23, 22, 24, 21, 20, 19, 16, 18, 17, 14, 13, 15, 10, 12, 11 ], 
  [ 9, 8, 7, 5, 4, 6, 2, 1, 3, 25, 27, 26, 22, 24, 23, 20, 19, 21, 18, 17, 16, 13, 15, 14, 12, 11, 10 ], 
  [ 4, 6, 5, 2, 1, 3, 7, 9, 8, 24, 23, 22, 19, 21, 20, 27, 26, 25, 15, 14, 13, 10, 12, 11, 18, 17, 16 ], 
  [ 6, 5, 4, 1, 3, 2, 9, 8, 7, 23, 22, 24, 21, 20, 19, 26, 25, 27, 14, 13, 15, 12, 11, 10, 17, 16, 18 ], 
  [ 5, 4, 6, 3, 2, 1, 8, 7, 9, 22, 24, 23, 20, 19, 21, 25, 27, 26, 13, 15, 14, 11, 10, 12, 16, 18, 17 ], 
  [ 19, 21, 20, 26, 25, 27, 22, 24, 23, 10, 12, 11, 16, 18, 17, 14, 13, 15, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 21, 20, 19, 25, 27, 26, 24, 23, 22, 12, 11, 10, 18, 17, 16, 13, 15, 14, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 27, 26, 25, 23, 22, 24, 11, 10, 12, 17, 16, 18, 15, 14, 13, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 27, 26, 25, 22, 24, 23, 21, 20, 19, 17, 16, 18, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 2, 1, 3 ], 
  [ 26, 25, 27, 24, 23, 22, 20, 19, 21, 16, 18, 17, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 1, 3, 2 ], 
  [ 25, 27, 26, 23, 22, 24, 19, 21, 20, 18, 17, 16, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 3, 2, 1 ], 
  [ 22, 24, 23, 20, 19, 21, 25, 27, 26, 13, 15, 14, 11, 10, 12, 16, 18, 17, 4, 6, 5, 2, 1, 3, 7, 9, 8 ], 
  [ 24, 23, 22, 19, 21, 20, 27, 26, 25, 15, 14, 13, 10, 12, 11, 18, 17, 16, 6, 5, 4, 1, 3, 2, 9, 8, 7 ], 
  [ 23, 22, 24, 21, 20, 19, 26, 25, 27, 14, 13, 15, 12, 11, 10, 17, 16, 18, 5, 4, 6, 3, 2, 1, 8, 7, 9 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 2, 1, 3, 9, 8, 7, 5, 4, 6, 19, 21, 20, 25, 27, 26, 23, 22, 24 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 1, 3, 2, 8, 7, 9, 4, 6, 5, 21, 20, 19, 27, 26, 25, 22, 24, 23 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 3, 2, 1, 7, 9, 8, 6, 5, 4, 20, 19, 21, 26, 25, 27, 24, 23, 22 ], 
  [ 17, 16, 18, 14, 13, 15, 12, 11, 10, 7, 9, 8, 5, 4, 6, 1, 3, 2, 26, 25, 27, 22, 24, 23, 19, 21, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 11, 10, 12, 9, 8, 7, 4, 6, 5, 3, 2, 1, 25, 27, 26, 24, 23, 22, 21, 20, 19 ], 
  [ 18, 17, 16, 15, 14, 13, 10, 12, 11, 8, 7, 9, 6, 5, 4, 2, 1, 3, 27, 26, 25, 23, 22, 24, 20, 19, 21 ], 
  [ 14, 13, 15, 12, 11, 10, 17, 16, 18, 5, 4, 6, 3, 2, 1, 8, 7, 9, 22, 24, 23, 20, 19, 21, 25, 27, 26 ], 
  [ 13, 15, 14, 11, 10, 12, 16, 18, 17, 4, 6, 5, 2, 1, 3, 7, 9, 8, 24, 23, 22, 19, 21, 20, 27, 26, 25 ], 
  [ 15, 14, 13, 10, 12, 11, 18, 17, 16, 6, 5, 4, 1, 3, 2, 9, 8, 7, 23, 22, 24, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 13;
QUANDLES[27].rack[13] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 21, 20, 19, 25, 27, 26, 24, 23, 22, 12, 11, 10, 18, 17, 16, 13, 15, 14 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 20, 19, 21, 27, 26, 25, 23, 22, 24, 11, 10, 12, 17, 16, 18, 15, 14, 13 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 19, 21, 20, 26, 25, 27, 22, 24, 23, 10, 12, 11, 16, 18, 17, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 3, 2, 1, 25, 27, 26, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 10, 12, 11 ], 
  [ 8, 7, 9, 6, 5, 4, 2, 1, 3, 27, 26, 25, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 12, 11, 10 ], 
  [ 7, 9, 8, 5, 4, 6, 1, 3, 2, 26, 25, 27, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 11, 10, 12 ], 
  [ 6, 5, 4, 3, 2, 1, 7, 9, 8, 23, 22, 24, 20, 19, 21, 27, 26, 25, 14, 13, 15, 11, 10, 12, 18, 17, 16 ], 
  [ 5, 4, 6, 2, 1, 3, 9, 8, 7, 22, 24, 23, 19, 21, 20, 26, 25, 27, 13, 15, 14, 10, 12, 11, 17, 16, 18 ], 
  [ 4, 6, 5, 1, 3, 2, 8, 7, 9, 24, 23, 22, 21, 20, 19, 25, 27, 26, 15, 14, 13, 12, 11, 10, 16, 18, 17 ], 
  [ 19, 21, 20, 25, 27, 26, 23, 22, 24, 10, 12, 11, 18, 17, 16, 15, 14, 13, 1, 3, 2, 8, 7, 9, 4, 6, 5 ], 
  [ 21, 20, 19, 27, 26, 25, 22, 24, 23, 12, 11, 10, 17, 16, 18, 14, 13, 15, 3, 2, 1, 7, 9, 8, 6, 5, 4 ], 
  [ 20, 19, 21, 26, 25, 27, 24, 23, 22, 11, 10, 12, 16, 18, 17, 13, 15, 14, 2, 1, 3, 9, 8, 7, 5, 4, 6 ], 
  [ 25, 27, 26, 22, 24, 23, 20, 19, 21, 18, 17, 16, 13, 15, 14, 12, 11, 10, 8, 7, 9, 4, 6, 5, 1, 3, 2 ], 
  [ 27, 26, 25, 24, 23, 22, 19, 21, 20, 17, 16, 18, 15, 14, 13, 11, 10, 12, 7, 9, 8, 6, 5, 4, 3, 2, 1 ], 
  [ 26, 25, 27, 23, 22, 24, 21, 20, 19, 16, 18, 17, 14, 13, 15, 10, 12, 11, 9, 8, 7, 5, 4, 6, 2, 1, 3 ], 
  [ 24, 23, 22, 21, 20, 19, 25, 27, 26, 15, 14, 13, 12, 11, 10, 16, 18, 17, 6, 5, 4, 3, 2, 1, 7, 9, 8 ], 
  [ 23, 22, 24, 20, 19, 21, 27, 26, 25, 14, 13, 15, 11, 10, 12, 18, 17, 16, 5, 4, 6, 2, 1, 3, 9, 8, 7 ], 
  [ 22, 24, 23, 19, 21, 20, 26, 25, 27, 13, 15, 14, 10, 12, 11, 17, 16, 18, 4, 6, 5, 1, 3, 2, 8, 7, 9 ], 
  [ 11, 10, 12, 18, 17, 16, 14, 13, 15, 2, 1, 3, 8, 7, 9, 6, 5, 4, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 10, 12, 11, 17, 16, 18, 13, 15, 14, 1, 3, 2, 7, 9, 8, 5, 4, 6, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 12, 11, 10, 16, 18, 17, 15, 14, 13, 3, 2, 1, 9, 8, 7, 4, 6, 5, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 18, 17, 16, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 3, 2, 1, 27, 26, 25, 22, 24, 23, 21, 20, 19 ], 
  [ 17, 16, 18, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 2, 1, 3, 26, 25, 27, 24, 23, 22, 20, 19, 21 ], 
  [ 16, 18, 17, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 1, 3, 2, 25, 27, 26, 23, 22, 24, 19, 21, 20 ], 
  [ 13, 15, 14, 10, 12, 11, 17, 16, 18, 4, 6, 5, 1, 3, 2, 8, 7, 9, 24, 23, 22, 21, 20, 19, 25, 27, 26 ], 
  [ 15, 14, 13, 12, 11, 10, 16, 18, 17, 6, 5, 4, 3, 2, 1, 7, 9, 8, 23, 22, 24, 20, 19, 21, 27, 26, 25 ], 
  [ 14, 13, 15, 11, 10, 12, 18, 17, 16, 5, 4, 6, 2, 1, 3, 9, 8, 7, 22, 24, 23, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 14;
QUANDLES[27].rack[14] := rec( size := 27, matrix :=
[ [ 1, 4, 7, 2, 5, 8, 3, 6, 9, 20, 23, 26, 21, 24, 27, 19, 22, 25, 17, 11, 14, 18, 12, 15, 16, 10, 13 ], 
  [ 8, 2, 5, 9, 3, 6, 7, 1, 4, 19, 22, 25, 20, 23, 26, 21, 24, 27, 11, 14, 17, 12, 15, 18, 10, 13, 16 ], 
  [ 6, 9, 3, 4, 7, 1, 5, 8, 2, 21, 24, 27, 19, 22, 25, 20, 23, 26, 14, 17, 11, 15, 18, 12, 13, 16, 10 ], 
  [ 6, 9, 3, 4, 7, 1, 5, 8, 2, 21, 24, 27, 19, 22, 25, 20, 23, 26, 14, 17, 11, 15, 18, 12, 13, 16, 10 ], 
  [ 1, 4, 7, 2, 5, 8, 3, 6, 9, 20, 23, 26, 21, 24, 27, 19, 22, 25, 17, 11, 14, 18, 12, 15, 16, 10, 13 ], 
  [ 8, 2, 5, 9, 3, 6, 7, 1, 4, 19, 22, 25, 20, 23, 26, 21, 24, 27, 11, 14, 17, 12, 15, 18, 10, 13, 16 ], 
  [ 8, 2, 5, 9, 3, 6, 7, 1, 4, 19, 22, 25, 20, 23, 26, 21, 24, 27, 11, 14, 17, 12, 15, 18, 10, 13, 16 ], 
  [ 6, 9, 3, 4, 7, 1, 5, 8, 2, 21, 24, 27, 19, 22, 25, 20, 23, 26, 14, 17, 11, 15, 18, 12, 13, 16, 10 ], 
  [ 1, 4, 7, 2, 5, 8, 3, 6, 9, 20, 23, 26, 21, 24, 27, 19, 22, 25, 17, 11, 14, 18, 12, 15, 16, 10, 13 ], 
  [ 26, 20, 23, 27, 21, 24, 25, 19, 22, 10, 13, 16, 11, 14, 17, 12, 15, 18, 2, 5, 8, 3, 6, 9, 1, 4, 7 ], 
  [ 20, 23, 26, 21, 24, 27, 19, 22, 25, 17, 11, 14, 18, 12, 15, 16, 10, 13, 1, 4, 7, 2, 5, 8, 3, 6, 9 ], 
  [ 23, 26, 20, 24, 27, 21, 22, 25, 19, 15, 18, 12, 13, 16, 10, 14, 17, 11, 3, 6, 9, 1, 4, 7, 2, 5, 8 ], 
  [ 23, 26, 20, 24, 27, 21, 22, 25, 19, 15, 18, 12, 13, 16, 10, 14, 17, 11, 3, 6, 9, 1, 4, 7, 2, 5, 8 ], 
  [ 26, 20, 23, 27, 21, 24, 25, 19, 22, 10, 13, 16, 11, 14, 17, 12, 15, 18, 2, 5, 8, 3, 6, 9, 1, 4, 7 ], 
  [ 20, 23, 26, 21, 24, 27, 19, 22, 25, 17, 11, 14, 18, 12, 15, 16, 10, 13, 1, 4, 7, 2, 5, 8, 3, 6, 9 ], 
  [ 20, 23, 26, 21, 24, 27, 19, 22, 25, 17, 11, 14, 18, 12, 15, 16, 10, 13, 1, 4, 7, 2, 5, 8, 3, 6, 9 ], 
  [ 23, 26, 20, 24, 27, 21, 22, 25, 19, 15, 18, 12, 13, 16, 10, 14, 17, 11, 3, 6, 9, 1, 4, 7, 2, 5, 8 ], 
  [ 26, 20, 23, 27, 21, 24, 25, 19, 22, 10, 13, 16, 11, 14, 17, 12, 15, 18, 2, 5, 8, 3, 6, 9, 1, 4, 7 ], 
  [ 11, 14, 17, 12, 15, 18, 10, 13, 16, 8, 2, 5, 9, 3, 6, 7, 1, 4, 19, 22, 25, 20, 23, 26, 21, 24, 27 ], 
  [ 10, 13, 16, 11, 14, 17, 12, 15, 18, 2, 5, 8, 3, 6, 9, 1, 4, 7, 26, 20, 23, 27, 21, 24, 25, 19, 22 ], 
  [ 12, 15, 18, 10, 13, 16, 11, 14, 17, 5, 8, 2, 6, 9, 3, 4, 7, 1, 24, 27, 21, 22, 25, 19, 23, 26, 20 ], 
  [ 12, 15, 18, 10, 13, 16, 11, 14, 17, 5, 8, 2, 6, 9, 3, 4, 7, 1, 24, 27, 21, 22, 25, 19, 23, 26, 20 ], 
  [ 11, 14, 17, 12, 15, 18, 10, 13, 16, 8, 2, 5, 9, 3, 6, 7, 1, 4, 19, 22, 25, 20, 23, 26, 21, 24, 27 ], 
  [ 10, 13, 16, 11, 14, 17, 12, 15, 18, 2, 5, 8, 3, 6, 9, 1, 4, 7, 26, 20, 23, 27, 21, 24, 25, 19, 22 ], 
  [ 10, 13, 16, 11, 14, 17, 12, 15, 18, 2, 5, 8, 3, 6, 9, 1, 4, 7, 26, 20, 23, 27, 21, 24, 25, 19, 22 ], 
  [ 12, 15, 18, 10, 13, 16, 11, 14, 17, 5, 8, 2, 6, 9, 3, 4, 7, 1, 24, 27, 21, 22, 25, 19, 23, 26, 20 ], 
  [ 11, 14, 17, 12, 15, 18, 10, 13, 16, 8, 2, 5, 9, 3, 6, 7, 1, 4, 19, 22, 25, 20, 23, 26, 21, 24, 27 ] ]);
QUANDLES[27].implemented := 15;
QUANDLES[27].rack[15] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 20, 19, 21, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 10, 12, 11, 16, 18, 17, 13, 15, 14, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 11, 10, 12, 17, 16, 18, 14, 13, 15, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 18, 17, 16, 15, 14, 13, 12, 11, 10, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 17, 16, 18, 14, 13, 15, 11, 10, 12, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 13, 15, 14, 10, 12, 11, 16, 18, 17, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 15, 14, 13, 12, 11, 10, 18, 17, 16, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 16;
QUANDLES[27].rack[16] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 25, 27, 26, 22, 24, 23, 19, 21, 20, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 22, 24, 23, 19, 21, 20, 25, 27, 26, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 26, 25, 27, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 21, 26, 25, 27, 23, 22, 24, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 27, 26, 25, 24, 23, 22, 21, 20, 19, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 24, 23, 22, 21, 20, 19, 27, 26, 25, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 21, 20, 19, 27, 26, 25, 24, 23, 22, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 12, 11, 10, 18, 17, 16, 15, 14, 13, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 16, 18, 17, 13, 15, 14, 10, 12, 11, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 10, 12, 11, 16, 18, 17, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 15, 14, 13, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 14, 13, 15, 11, 10, 12, 17, 16, 18, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 8, 7, 9, 5, 4, 6, 2, 1, 3, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 5, 4, 6, 2, 1, 3, 8, 7, 9, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 2, 1, 3, 8, 7, 9, 5, 4, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 3, 2, 1, 9, 8, 7, 6, 5, 4, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 6, 5, 4, 3, 2, 1, 9, 8, 7, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 1, 3, 2, 7, 9, 8, 4, 6, 5, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 17;
QUANDLES[27].rack[17] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 19, 21, 20, 27, 26, 25, 24, 23, 22, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 21, 20, 19, 26, 25, 27, 23, 22, 24, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 20, 19, 21, 25, 27, 26, 22, 24, 23, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 23, 22, 24, 20, 19, 21, 25, 27, 26, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 22, 24, 23, 19, 21, 20, 27, 26, 25, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 24, 23, 22, 21, 20, 19, 26, 25, 27, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 10, 12, 11, 18, 17, 16, 15, 14, 13, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 12, 11, 10, 17, 16, 18, 14, 13, 15, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 11, 10, 12, 16, 18, 17, 13, 15, 14, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 14, 13, 15, 11, 10, 12, 16, 18, 17, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 13, 15, 14, 10, 12, 11, 18, 17, 16, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 15, 14, 13, 12, 11, 10, 17, 16, 18, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 1, 3, 2, 9, 8, 7, 6, 5, 4, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 3, 2, 1, 8, 7, 9, 5, 4, 6, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 2, 1, 3, 7, 9, 8, 4, 6, 5, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 5, 4, 6, 2, 1, 3, 7, 9, 8, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 4, 6, 5, 1, 3, 2, 9, 8, 7, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 6, 5, 4, 3, 2, 1, 8, 7, 9, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 18;
QUANDLES[27].rack[18] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 26, 25, 27, 23, 22, 24, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 25, 27, 26, 22, 24, 23, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 27, 26, 25, 24, 23, 22, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 24, 23, 22, 21, 20, 19, 26, 25, 27, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 24, 20, 19, 21, 25, 27, 26, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 22, 24, 23, 19, 21, 20, 27, 26, 25, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 19, 21, 20, 27, 26, 25, 24, 23, 22, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 21, 20, 19, 26, 25, 27, 23, 22, 24, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 20, 19, 21, 25, 27, 26, 22, 24, 23, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 10, 12, 11, 18, 17, 16, 15, 14, 13, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 12, 11, 10, 17, 16, 18, 14, 13, 15, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 11, 10, 12, 16, 18, 17, 13, 15, 14, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 14, 13, 15, 11, 10, 12, 16, 18, 17, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 13, 15, 14, 10, 12, 11, 18, 17, 16, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 15, 14, 13, 12, 11, 10, 17, 16, 18, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 5, 4, 6, 2, 1, 3, 7, 9, 8, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 4, 6, 5, 1, 3, 2, 9, 8, 7, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 6, 5, 4, 3, 2, 1, 8, 7, 9, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 3, 2, 1, 8, 7, 9, 5, 4, 6, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 2, 1, 3, 7, 9, 8, 4, 6, 5, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 1, 3, 2, 9, 8, 7, 6, 5, 4, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 19;
QUANDLES[27].rack[19] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 25, 27, 26, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 27, 26, 25, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 26, 25, 27, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 21, 20, 19, 26, 25, 27, 23, 22, 24, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 20, 19, 21, 25, 27, 26, 22, 24, 23, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 19, 21, 20, 27, 26, 25, 24, 23, 22, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 10, 12, 11, 18, 17, 16, 15, 14, 13, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 12, 11, 10, 17, 16, 18, 14, 13, 15, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 11, 10, 12, 16, 18, 17, 13, 15, 14, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 14, 13, 15, 11, 10, 12, 16, 18, 17, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 13, 15, 14, 10, 12, 11, 18, 17, 16, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 15, 14, 13, 12, 11, 10, 17, 16, 18, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 6, 5, 4, 3, 2, 1, 8, 7, 9, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 5, 4, 6, 2, 1, 3, 7, 9, 8, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 4, 6, 5, 1, 3, 2, 9, 8, 7, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 1, 3, 2, 9, 8, 7, 6, 5, 4, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 3, 2, 1, 8, 7, 9, 5, 4, 6, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 2, 1, 3, 7, 9, 8, 4, 6, 5, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 20;
QUANDLES[27].rack[20] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 8, 7, 9, 5, 4, 6, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 7, 9, 8, 4, 6, 5, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 9, 8, 7, 6, 5, 4, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 21;
QUANDLES[27].rack[21] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 24, 23, 19, 21, 20, 25, 27, 26, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 24, 23, 22, 21, 20, 19, 27, 26, 25, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 10, 12, 11, 16, 18, 17, 13, 15, 14, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 12, 11, 10, 18, 17, 16, 15, 14, 13, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 11, 10, 12, 17, 16, 18, 14, 13, 15, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 13, 15, 14, 10, 12, 11, 16, 18, 17, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 15, 14, 13, 12, 11, 10, 18, 17, 16, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 14, 13, 15, 11, 10, 12, 17, 16, 18, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 2, 1, 3, 8, 7, 9, 5, 4, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 6, 5, 4, 3, 2, 1, 9, 8, 7, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 22;
QUANDLES[27].rack[22] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 9, 8, 7, 6, 5, 4, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 8, 7, 9, 5, 4, 6, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 7, 9, 8, 4, 6, 5, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 23;
QUANDLES[27].rack[23] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 4, 6, 5, 1, 3, 2, 7, 9, 8, 23, 22, 24, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 3, 2, 1, 9, 8, 7, 22, 24, 23, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 5, 4, 6, 2, 1, 3, 8, 7, 9, 24, 23, 22, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 9, 8, 7, 6, 5, 4, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 8, 7, 9, 5, 4, 6, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 7, 9, 8, 4, 6, 5, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7, 22, 24, 23, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9, 24, 23, 22, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8, 23, 22, 24, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 24;
QUANDLES[27].rack[24] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 26, 25, 27, 23, 22, 24, 20, 19, 21, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 25, 27, 26, 22, 24, 23, 19, 21, 20, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 27, 26, 25, 24, 23, 22, 21, 20, 19, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 2, 1, 3, 23, 22, 24, 20, 19, 21, 26, 25, 27, 16, 18, 17, 15, 14, 13, 11, 10, 12 ], 
  [ 8, 7, 9, 6, 5, 4, 1, 3, 2, 22, 24, 23, 19, 21, 20, 25, 27, 26, 18, 17, 16, 14, 13, 15, 10, 12, 11 ], 
  [ 7, 9, 8, 5, 4, 6, 3, 2, 1, 24, 23, 22, 21, 20, 19, 27, 26, 25, 17, 16, 18, 13, 15, 14, 12, 11, 10 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 20, 19, 21, 26, 25, 27, 23, 22, 24, 14, 13, 15, 10, 12, 11, 18, 17, 16 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 19, 21, 20, 25, 27, 26, 22, 24, 23, 13, 15, 14, 12, 11, 10, 17, 16, 18 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 21, 20, 19, 27, 26, 25, 24, 23, 22, 15, 14, 13, 11, 10, 12, 16, 18, 17 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 10, 12, 11, 17, 16, 18, 15, 14, 13, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 12, 11, 10, 16, 18, 17, 14, 13, 15, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 11, 10, 12, 18, 17, 16, 13, 15, 14, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 26, 25, 27, 22, 24, 23, 21, 20, 19, 18, 17, 16, 13, 15, 14, 11, 10, 12, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 25, 27, 26, 24, 23, 22, 20, 19, 21, 17, 16, 18, 15, 14, 13, 10, 12, 11, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 27, 26, 25, 23, 22, 24, 19, 21, 20, 16, 18, 17, 14, 13, 15, 12, 11, 10, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 24, 23, 22, 20, 19, 21, 25, 27, 26, 14, 13, 15, 12, 11, 10, 16, 18, 17, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 23, 22, 24, 19, 21, 20, 27, 26, 25, 13, 15, 14, 11, 10, 12, 18, 17, 16, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 22, 24, 23, 21, 20, 19, 26, 25, 27, 15, 14, 13, 10, 12, 11, 17, 16, 18, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 6, 5, 4, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 5, 4, 6, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 4, 6, 5, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 9, 8, 7, 5, 4, 6, 1, 3, 2, 27, 26, 25, 22, 24, 23, 20, 19, 21 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 8, 7, 9, 4, 6, 5, 3, 2, 1, 26, 25, 27, 24, 23, 22, 19, 21, 20 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 7, 9, 8, 6, 5, 4, 2, 1, 3, 25, 27, 26, 23, 22, 24, 21, 20, 19 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 4, 6, 5, 3, 2, 1, 8, 7, 9, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 6, 5, 4, 2, 1, 3, 7, 9, 8, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 5, 4, 6, 1, 3, 2, 9, 8, 7, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 25;
QUANDLES[27].rack[25] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 13, 15, 14, 25, 27, 26, 9, 8, 7, 10, 12, 11, 22, 24, 23, 6, 5, 4, 18, 17, 16, 19, 21, 20 ], 
  [ 3, 2, 1, 15, 14, 13, 27, 26, 25, 8, 7, 9, 12, 11, 10, 24, 23, 22, 5, 4, 6, 17, 16, 18, 21, 20, 19 ], 
  [ 2, 1, 3, 14, 13, 15, 26, 25, 27, 7, 9, 8, 11, 10, 12, 23, 22, 24, 4, 6, 5, 16, 18, 17, 20, 19, 21 ], 
  [ 21, 20, 19, 4, 6, 5, 16, 18, 17, 26, 25, 27, 1, 3, 2, 13, 15, 14, 23, 22, 24, 9, 8, 7, 10, 12, 11 ], 
  [ 20, 19, 21, 6, 5, 4, 18, 17, 16, 25, 27, 26, 3, 2, 1, 15, 14, 13, 22, 24, 23, 8, 7, 9, 12, 11, 10 ], 
  [ 19, 21, 20, 5, 4, 6, 17, 16, 18, 27, 26, 25, 2, 1, 3, 14, 13, 15, 24, 23, 22, 7, 9, 8, 11, 10, 12 ], 
  [ 12, 11, 10, 24, 23, 22, 7, 9, 8, 17, 16, 18, 21, 20, 19, 4, 6, 5, 14, 13, 15, 26, 25, 27, 1, 3, 2 ], 
  [ 11, 10, 12, 23, 22, 24, 9, 8, 7, 16, 18, 17, 20, 19, 21, 6, 5, 4, 13, 15, 14, 25, 27, 26, 3, 2, 1 ], 
  [ 10, 12, 11, 22, 24, 23, 8, 7, 9, 18, 17, 16, 19, 21, 20, 5, 4, 6, 15, 14, 13, 27, 26, 25, 2, 1, 3 ], 
  [ 13, 15, 14, 25, 27, 26, 3, 2, 1, 10, 12, 11, 22, 24, 23, 8, 7, 9, 18, 17, 16, 19, 21, 20, 5, 4, 6 ], 
  [ 15, 14, 13, 27, 26, 25, 2, 1, 3, 12, 11, 10, 24, 23, 22, 7, 9, 8, 17, 16, 18, 21, 20, 19, 4, 6, 5 ], 
  [ 14, 13, 15, 26, 25, 27, 1, 3, 2, 11, 10, 12, 23, 22, 24, 9, 8, 7, 16, 18, 17, 20, 19, 21, 6, 5, 4 ], 
  [ 4, 6, 5, 16, 18, 17, 20, 19, 21, 1, 3, 2, 13, 15, 14, 25, 27, 26, 9, 8, 7, 10, 12, 11, 22, 24, 23 ], 
  [ 6, 5, 4, 18, 17, 16, 19, 21, 20, 3, 2, 1, 15, 14, 13, 27, 26, 25, 8, 7, 9, 12, 11, 10, 24, 23, 22 ], 
  [ 5, 4, 6, 17, 16, 18, 21, 20, 19, 2, 1, 3, 14, 13, 15, 26, 25, 27, 7, 9, 8, 11, 10, 12, 23, 22, 24 ], 
  [ 24, 23, 22, 7, 9, 8, 11, 10, 12, 21, 20, 19, 4, 6, 5, 16, 18, 17, 26, 25, 27, 1, 3, 2, 13, 15, 14 ], 
  [ 23, 22, 24, 9, 8, 7, 10, 12, 11, 20, 19, 21, 6, 5, 4, 18, 17, 16, 25, 27, 26, 3, 2, 1, 15, 14, 13 ], 
  [ 22, 24, 23, 8, 7, 9, 12, 11, 10, 19, 21, 20, 5, 4, 6, 17, 16, 18, 27, 26, 25, 2, 1, 3, 14, 13, 15 ], 
  [ 25, 27, 26, 3, 2, 1, 15, 14, 13, 22, 24, 23, 8, 7, 9, 12, 11, 10, 19, 21, 20, 5, 4, 6, 17, 16, 18 ], 
  [ 27, 26, 25, 2, 1, 3, 14, 13, 15, 24, 23, 22, 7, 9, 8, 11, 10, 12, 21, 20, 19, 4, 6, 5, 16, 18, 17 ], 
  [ 26, 25, 27, 1, 3, 2, 13, 15, 14, 23, 22, 24, 9, 8, 7, 10, 12, 11, 20, 19, 21, 6, 5, 4, 18, 17, 16 ], 
  [ 16, 18, 17, 20, 19, 21, 6, 5, 4, 13, 15, 14, 25, 27, 26, 3, 2, 1, 10, 12, 11, 22, 24, 23, 8, 7, 9 ], 
  [ 18, 17, 16, 19, 21, 20, 5, 4, 6, 15, 14, 13, 27, 26, 25, 2, 1, 3, 12, 11, 10, 24, 23, 22, 7, 9, 8 ], 
  [ 17, 16, 18, 21, 20, 19, 4, 6, 5, 14, 13, 15, 26, 25, 27, 1, 3, 2, 11, 10, 12, 23, 22, 24, 9, 8, 7 ], 
  [ 7, 9, 8, 11, 10, 12, 23, 22, 24, 4, 6, 5, 16, 18, 17, 20, 19, 21, 1, 3, 2, 13, 15, 14, 25, 27, 26 ], 
  [ 9, 8, 7, 10, 12, 11, 22, 24, 23, 6, 5, 4, 18, 17, 16, 19, 21, 20, 3, 2, 1, 15, 14, 13, 27, 26, 25 ], 
  [ 8, 7, 9, 12, 11, 10, 24, 23, 22, 5, 4, 6, 17, 16, 18, 21, 20, 19, 2, 1, 3, 14, 13, 15, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 26;
QUANDLES[27].rack[26] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 6, 5, 4, 26, 25, 27, 24, 23, 22, 21, 20, 19, 14, 13, 15, 10, 12, 11, 17, 16, 18 ], 
  [ 3, 2, 1, 9, 8, 7, 5, 4, 6, 25, 27, 26, 23, 22, 24, 20, 19, 21, 13, 15, 14, 12, 11, 10, 16, 18, 17 ], 
  [ 2, 1, 3, 8, 7, 9, 4, 6, 5, 27, 26, 25, 22, 24, 23, 19, 21, 20, 15, 14, 13, 11, 10, 12, 18, 17, 16 ], 
  [ 9, 8, 7, 4, 6, 5, 1, 3, 2, 23, 22, 24, 19, 21, 20, 26, 25, 27, 12, 11, 10, 18, 17, 16, 14, 13, 15 ], 
  [ 8, 7, 9, 6, 5, 4, 3, 2, 1, 22, 24, 23, 21, 20, 19, 25, 27, 26, 11, 10, 12, 17, 16, 18, 13, 15, 14 ], 
  [ 7, 9, 8, 5, 4, 6, 2, 1, 3, 24, 23, 22, 20, 19, 21, 27, 26, 25, 10, 12, 11, 16, 18, 17, 15, 14, 13 ], 
  [ 4, 6, 5, 3, 2, 1, 7, 9, 8, 19, 21, 20, 25, 27, 26, 24, 23, 22, 18, 17, 16, 13, 15, 14, 10, 12, 11 ], 
  [ 6, 5, 4, 2, 1, 3, 9, 8, 7, 21, 20, 19, 27, 26, 25, 23, 22, 24, 17, 16, 18, 15, 14, 13, 12, 11, 10 ], 
  [ 5, 4, 6, 1, 3, 2, 8, 7, 9, 20, 19, 21, 26, 25, 27, 22, 24, 23, 16, 18, 17, 14, 13, 15, 11, 10, 12 ], 
  [ 24, 23, 22, 20, 19, 21, 27, 26, 25, 10, 12, 11, 16, 18, 17, 15, 14, 13, 9, 8, 7, 4, 6, 5, 1, 3, 2 ], 
  [ 23, 22, 24, 19, 21, 20, 26, 25, 27, 12, 11, 10, 18, 17, 16, 14, 13, 15, 8, 7, 9, 6, 5, 4, 3, 2, 1 ], 
  [ 22, 24, 23, 21, 20, 19, 25, 27, 26, 11, 10, 12, 17, 16, 18, 13, 15, 14, 7, 9, 8, 5, 4, 6, 2, 1, 3 ], 
  [ 19, 21, 20, 25, 27, 26, 24, 23, 22, 18, 17, 16, 13, 15, 14, 10, 12, 11, 6, 5, 4, 2, 1, 3, 9, 8, 7 ], 
  [ 21, 20, 19, 27, 26, 25, 23, 22, 24, 17, 16, 18, 15, 14, 13, 12, 11, 10, 5, 4, 6, 1, 3, 2, 8, 7, 9 ], 
  [ 20, 19, 21, 26, 25, 27, 22, 24, 23, 16, 18, 17, 14, 13, 15, 11, 10, 12, 4, 6, 5, 3, 2, 1, 7, 9, 8 ], 
  [ 25, 27, 26, 23, 22, 24, 20, 19, 21, 13, 15, 14, 12, 11, 10, 16, 18, 17, 2, 1, 3, 8, 7, 9, 4, 6, 5 ], 
  [ 27, 26, 25, 22, 24, 23, 19, 21, 20, 15, 14, 13, 11, 10, 12, 18, 17, 16, 1, 3, 2, 7, 9, 8, 6, 5, 4 ], 
  [ 26, 25, 27, 24, 23, 22, 21, 20, 19, 14, 13, 15, 10, 12, 11, 17, 16, 18, 3, 2, 1, 9, 8, 7, 5, 4, 6 ], 
  [ 16, 18, 17, 14, 13, 15, 11, 10, 12, 4, 6, 5, 3, 2, 1, 7, 9, 8, 19, 21, 20, 25, 27, 26, 24, 23, 22 ], 
  [ 18, 17, 16, 13, 15, 14, 10, 12, 11, 6, 5, 4, 2, 1, 3, 9, 8, 7, 21, 20, 19, 27, 26, 25, 23, 22, 24 ], 
  [ 17, 16, 18, 15, 14, 13, 12, 11, 10, 5, 4, 6, 1, 3, 2, 8, 7, 9, 20, 19, 21, 26, 25, 27, 22, 24, 23 ], 
  [ 13, 15, 14, 12, 11, 10, 16, 18, 17, 2, 1, 3, 8, 7, 9, 4, 6, 5, 27, 26, 25, 22, 24, 23, 19, 21, 20 ], 
  [ 15, 14, 13, 11, 10, 12, 18, 17, 16, 1, 3, 2, 7, 9, 8, 6, 5, 4, 26, 25, 27, 24, 23, 22, 21, 20, 19 ], 
  [ 14, 13, 15, 10, 12, 11, 17, 16, 18, 3, 2, 1, 9, 8, 7, 5, 4, 6, 25, 27, 26, 23, 22, 24, 20, 19, 21 ], 
  [ 12, 11, 10, 18, 17, 16, 14, 13, 15, 8, 7, 9, 6, 5, 4, 3, 2, 1, 22, 24, 23, 21, 20, 19, 25, 27, 26 ], 
  [ 11, 10, 12, 17, 16, 18, 13, 15, 14, 7, 9, 8, 5, 4, 6, 2, 1, 3, 24, 23, 22, 20, 19, 21, 27, 26, 25 ], 
  [ 10, 12, 11, 16, 18, 17, 15, 14, 13, 9, 8, 7, 4, 6, 5, 1, 3, 2, 23, 22, 24, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 27;
QUANDLES[27].rack[27] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 18, 17, 16, 24, 23, 22, 6, 5, 4, 10, 12, 11, 27, 26, 25, 8, 7, 9, 14, 13, 15, 21, 20, 19 ], 
  [ 3, 2, 1, 17, 16, 18, 23, 22, 24, 5, 4, 6, 12, 11, 10, 26, 25, 27, 7, 9, 8, 13, 15, 14, 20, 19, 21 ], 
  [ 2, 1, 3, 16, 18, 17, 22, 24, 23, 4, 6, 5, 11, 10, 12, 25, 27, 26, 9, 8, 7, 15, 14, 13, 19, 21, 20 ], 
  [ 25, 27, 26, 4, 6, 5, 11, 10, 12, 21, 20, 19, 8, 7, 9, 14, 13, 15, 23, 22, 24, 3, 2, 1, 17, 16, 18 ], 
  [ 27, 26, 25, 6, 5, 4, 10, 12, 11, 20, 19, 21, 7, 9, 8, 13, 15, 14, 22, 24, 23, 2, 1, 3, 16, 18, 17 ], 
  [ 26, 25, 27, 5, 4, 6, 12, 11, 10, 19, 21, 20, 9, 8, 7, 15, 14, 13, 24, 23, 22, 1, 3, 2, 18, 17, 16 ], 
  [ 13, 15, 14, 20, 19, 21, 7, 9, 8, 18, 17, 16, 24, 23, 22, 1, 3, 2, 11, 10, 12, 25, 27, 26, 4, 6, 5 ], 
  [ 15, 14, 13, 19, 21, 20, 9, 8, 7, 17, 16, 18, 23, 22, 24, 3, 2, 1, 10, 12, 11, 27, 26, 25, 6, 5, 4 ], 
  [ 14, 13, 15, 21, 20, 19, 8, 7, 9, 16, 18, 17, 22, 24, 23, 2, 1, 3, 12, 11, 10, 26, 25, 27, 5, 4, 6 ], 
  [ 17, 16, 18, 23, 22, 24, 3, 2, 1, 10, 12, 11, 27, 26, 25, 6, 5, 4, 15, 14, 13, 19, 21, 20, 9, 8, 7 ], 
  [ 16, 18, 17, 22, 24, 23, 2, 1, 3, 12, 11, 10, 26, 25, 27, 5, 4, 6, 14, 13, 15, 21, 20, 19, 8, 7, 9 ], 
  [ 18, 17, 16, 24, 23, 22, 1, 3, 2, 11, 10, 12, 25, 27, 26, 4, 6, 5, 13, 15, 14, 20, 19, 21, 7, 9, 8 ], 
  [ 5, 4, 6, 12, 11, 10, 26, 25, 27, 7, 9, 8, 13, 15, 14, 20, 19, 21, 3, 2, 1, 17, 16, 18, 23, 22, 24 ], 
  [ 4, 6, 5, 11, 10, 12, 25, 27, 26, 9, 8, 7, 15, 14, 13, 19, 21, 20, 2, 1, 3, 16, 18, 17, 22, 24, 23 ], 
  [ 6, 5, 4, 10, 12, 11, 27, 26, 25, 8, 7, 9, 14, 13, 15, 21, 20, 19, 1, 3, 2, 18, 17, 16, 24, 23, 22 ], 
  [ 20, 19, 21, 7, 9, 8, 13, 15, 14, 22, 24, 23, 2, 1, 3, 16, 18, 17, 27, 26, 25, 6, 5, 4, 10, 12, 11 ], 
  [ 19, 21, 20, 9, 8, 7, 15, 14, 13, 24, 23, 22, 1, 3, 2, 18, 17, 16, 26, 25, 27, 5, 4, 6, 12, 11, 10 ], 
  [ 21, 20, 19, 8, 7, 9, 14, 13, 15, 23, 22, 24, 3, 2, 1, 17, 16, 18, 25, 27, 26, 4, 6, 5, 11, 10, 12 ], 
  [ 24, 23, 22, 1, 3, 2, 18, 17, 16, 26, 25, 27, 5, 4, 6, 12, 11, 10, 19, 21, 20, 9, 8, 7, 15, 14, 13 ], 
  [ 23, 22, 24, 3, 2, 1, 17, 16, 18, 25, 27, 26, 4, 6, 5, 11, 10, 12, 21, 20, 19, 8, 7, 9, 14, 13, 15 ], 
  [ 22, 24, 23, 2, 1, 3, 16, 18, 17, 27, 26, 25, 6, 5, 4, 10, 12, 11, 20, 19, 21, 7, 9, 8, 13, 15, 14 ], 
  [ 12, 11, 10, 26, 25, 27, 5, 4, 6, 14, 13, 15, 21, 20, 19, 8, 7, 9, 16, 18, 17, 22, 24, 23, 2, 1, 3 ], 
  [ 11, 10, 12, 25, 27, 26, 4, 6, 5, 13, 15, 14, 20, 19, 21, 7, 9, 8, 18, 17, 16, 24, 23, 22, 1, 3, 2 ], 
  [ 10, 12, 11, 27, 26, 25, 6, 5, 4, 15, 14, 13, 19, 21, 20, 9, 8, 7, 17, 16, 18, 23, 22, 24, 3, 2, 1 ], 
  [ 9, 8, 7, 15, 14, 13, 19, 21, 20, 2, 1, 3, 16, 18, 17, 22, 24, 23, 4, 6, 5, 11, 10, 12, 25, 27, 26 ], 
  [ 8, 7, 9, 14, 13, 15, 21, 20, 19, 1, 3, 2, 18, 17, 16, 24, 23, 22, 6, 5, 4, 10, 12, 11, 27, 26, 25 ], 
  [ 7, 9, 8, 13, 15, 14, 20, 19, 21, 3, 2, 1, 17, 16, 18, 23, 22, 24, 5, 4, 6, 12, 11, 10, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 28;
QUANDLES[27].rack[28] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 22, 24, 23, 17, 16, 18, 8, 7, 9, 19, 21, 20, 13, 15, 14, 6, 5, 4, 25, 27, 26, 12, 11, 10 ], 
  [ 3, 2, 1, 24, 23, 22, 16, 18, 17, 7, 9, 8, 21, 20, 19, 15, 14, 13, 5, 4, 6, 27, 26, 25, 11, 10, 12 ], 
  [ 2, 1, 3, 23, 22, 24, 18, 17, 16, 9, 8, 7, 20, 19, 21, 14, 13, 15, 4, 6, 5, 26, 25, 27, 10, 12, 11 ], 
  [ 10, 12, 11, 4, 6, 5, 26, 25, 27, 17, 16, 18, 1, 3, 2, 22, 24, 23, 15, 14, 13, 7, 9, 8, 21, 20, 19 ], 
  [ 12, 11, 10, 6, 5, 4, 25, 27, 26, 16, 18, 17, 3, 2, 1, 24, 23, 22, 14, 13, 15, 9, 8, 7, 20, 19, 21 ], 
  [ 11, 10, 12, 5, 4, 6, 27, 26, 25, 18, 17, 16, 2, 1, 3, 23, 22, 24, 13, 15, 14, 8, 7, 9, 19, 21, 20 ], 
  [ 21, 20, 19, 15, 14, 13, 7, 9, 8, 25, 27, 26, 12, 11, 10, 6, 5, 4, 23, 22, 24, 18, 17, 16, 2, 1, 3 ], 
  [ 20, 19, 21, 14, 13, 15, 9, 8, 7, 27, 26, 25, 11, 10, 12, 5, 4, 6, 22, 24, 23, 17, 16, 18, 1, 3, 2 ], 
  [ 19, 21, 20, 13, 15, 14, 8, 7, 9, 26, 25, 27, 10, 12, 11, 4, 6, 5, 24, 23, 22, 16, 18, 17, 3, 2, 1 ], 
  [ 15, 14, 13, 7, 9, 8, 21, 20, 19, 10, 12, 11, 4, 6, 5, 26, 25, 27, 17, 16, 18, 1, 3, 2, 22, 24, 23 ], 
  [ 14, 13, 15, 9, 8, 7, 20, 19, 21, 12, 11, 10, 6, 5, 4, 25, 27, 26, 16, 18, 17, 3, 2, 1, 24, 23, 22 ], 
  [ 13, 15, 14, 8, 7, 9, 19, 21, 20, 11, 10, 12, 5, 4, 6, 27, 26, 25, 18, 17, 16, 2, 1, 3, 23, 22, 24 ], 
  [ 24, 23, 22, 16, 18, 17, 3, 2, 1, 19, 21, 20, 13, 15, 14, 8, 7, 9, 26, 25, 27, 10, 12, 11, 4, 6, 5 ], 
  [ 23, 22, 24, 18, 17, 16, 2, 1, 3, 21, 20, 19, 15, 14, 13, 7, 9, 8, 25, 27, 26, 12, 11, 10, 6, 5, 4 ], 
  [ 22, 24, 23, 17, 16, 18, 1, 3, 2, 20, 19, 21, 14, 13, 15, 9, 8, 7, 27, 26, 25, 11, 10, 12, 5, 4, 6 ], 
  [ 5, 4, 6, 27, 26, 25, 11, 10, 12, 3, 2, 1, 24, 23, 22, 16, 18, 17, 7, 9, 8, 21, 20, 19, 15, 14, 13 ], 
  [ 4, 6, 5, 26, 25, 27, 10, 12, 11, 2, 1, 3, 23, 22, 24, 18, 17, 16, 9, 8, 7, 20, 19, 21, 14, 13, 15 ], 
  [ 6, 5, 4, 25, 27, 26, 12, 11, 10, 1, 3, 2, 22, 24, 23, 17, 16, 18, 8, 7, 9, 19, 21, 20, 13, 15, 14 ], 
  [ 26, 25, 27, 10, 12, 11, 4, 6, 5, 24, 23, 22, 16, 18, 17, 3, 2, 1, 19, 21, 20, 13, 15, 14, 8, 7, 9 ], 
  [ 25, 27, 26, 12, 11, 10, 6, 5, 4, 23, 22, 24, 18, 17, 16, 2, 1, 3, 21, 20, 19, 15, 14, 13, 7, 9, 8 ], 
  [ 27, 26, 25, 11, 10, 12, 5, 4, 6, 22, 24, 23, 17, 16, 18, 1, 3, 2, 20, 19, 21, 14, 13, 15, 9, 8, 7 ], 
  [ 8, 7, 9, 19, 21, 20, 13, 15, 14, 6, 5, 4, 25, 27, 26, 12, 11, 10, 1, 3, 2, 22, 24, 23, 17, 16, 18 ], 
  [ 7, 9, 8, 21, 20, 19, 15, 14, 13, 5, 4, 6, 27, 26, 25, 11, 10, 12, 3, 2, 1, 24, 23, 22, 16, 18, 17 ], 
  [ 9, 8, 7, 20, 19, 21, 14, 13, 15, 4, 6, 5, 26, 25, 27, 10, 12, 11, 2, 1, 3, 23, 22, 24, 18, 17, 16 ], 
  [ 16, 18, 17, 3, 2, 1, 24, 23, 22, 14, 13, 15, 9, 8, 7, 20, 19, 21, 12, 11, 10, 6, 5, 4, 25, 27, 26 ], 
  [ 18, 17, 16, 2, 1, 3, 23, 22, 24, 13, 15, 14, 8, 7, 9, 19, 21, 20, 11, 10, 12, 5, 4, 6, 27, 26, 25 ], 
  [ 17, 16, 18, 1, 3, 2, 22, 24, 23, 15, 14, 13, 7, 9, 8, 21, 20, 19, 10, 12, 11, 4, 6, 5, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 29;
QUANDLES[27].rack[29] := rec( size := 27, matrix :=
[ [ 1, 7, 4, 9, 6, 3, 5, 2, 8, 25, 22, 19, 24, 21, 27, 20, 26, 23, 13, 10, 16, 12, 18, 15, 17, 14, 11 ], 
  [ 5, 2, 8, 1, 7, 4, 9, 6, 3, 20, 26, 23, 25, 22, 19, 24, 21, 27, 17, 14, 11, 13, 10, 16, 12, 18, 15 ], 
  [ 9, 6, 3, 5, 2, 8, 1, 7, 4, 24, 21, 27, 20, 26, 23, 25, 22, 19, 12, 18, 15, 17, 14, 11, 13, 10, 16 ], 
  [ 8, 5, 2, 4, 1, 7, 3, 9, 6, 23, 20, 26, 19, 25, 22, 27, 24, 21, 11, 17, 14, 16, 13, 10, 15, 12, 18 ], 
  [ 3, 9, 6, 8, 5, 2, 4, 1, 7, 27, 24, 21, 23, 20, 26, 19, 25, 22, 15, 12, 18, 11, 17, 14, 16, 13, 10 ], 
  [ 4, 1, 7, 3, 9, 6, 8, 5, 2, 19, 25, 22, 27, 24, 21, 23, 20, 26, 16, 13, 10, 15, 12, 18, 11, 17, 14 ], 
  [ 6, 3, 9, 2, 8, 5, 7, 4, 1, 21, 27, 24, 26, 23, 20, 22, 19, 25, 18, 15, 12, 14, 11, 17, 10, 16, 13 ], 
  [ 7, 4, 1, 6, 3, 9, 2, 8, 5, 22, 19, 25, 21, 27, 24, 26, 23, 20, 10, 16, 13, 18, 15, 12, 14, 11, 17 ], 
  [ 2, 8, 5, 7, 4, 1, 6, 3, 9, 26, 23, 20, 22, 19, 25, 21, 27, 24, 14, 11, 17, 10, 16, 13, 18, 15, 12 ], 
  [ 22, 19, 25, 21, 27, 24, 26, 23, 20, 10, 16, 13, 18, 15, 12, 14, 11, 17, 7, 4, 1, 6, 3, 9, 2, 8, 5 ], 
  [ 26, 23, 20, 22, 19, 25, 21, 27, 24, 14, 11, 17, 10, 16, 13, 18, 15, 12, 2, 8, 5, 7, 4, 1, 6, 3, 9 ], 
  [ 21, 27, 24, 26, 23, 20, 22, 19, 25, 18, 15, 12, 14, 11, 17, 10, 16, 13, 6, 3, 9, 2, 8, 5, 7, 4, 1 ], 
  [ 20, 26, 23, 25, 22, 19, 24, 21, 27, 17, 14, 11, 13, 10, 16, 12, 18, 15, 5, 2, 8, 1, 7, 4, 9, 6, 3 ], 
  [ 24, 21, 27, 20, 26, 23, 25, 22, 19, 12, 18, 15, 17, 14, 11, 13, 10, 16, 9, 6, 3, 5, 2, 8, 1, 7, 4 ], 
  [ 25, 22, 19, 24, 21, 27, 20, 26, 23, 13, 10, 16, 12, 18, 15, 17, 14, 11, 1, 7, 4, 9, 6, 3, 5, 2, 8 ], 
  [ 27, 24, 21, 23, 20, 26, 19, 25, 22, 15, 12, 18, 11, 17, 14, 16, 13, 10, 3, 9, 6, 8, 5, 2, 4, 1, 7 ], 
  [ 19, 25, 22, 27, 24, 21, 23, 20, 26, 16, 13, 10, 15, 12, 18, 11, 17, 14, 4, 1, 7, 3, 9, 6, 8, 5, 2 ], 
  [ 23, 20, 26, 19, 25, 22, 27, 24, 21, 11, 17, 14, 16, 13, 10, 15, 12, 18, 8, 5, 2, 4, 1, 7, 3, 9, 6 ], 
  [ 16, 13, 10, 15, 12, 18, 11, 17, 14, 4, 1, 7, 3, 9, 6, 8, 5, 2, 19, 25, 22, 27, 24, 21, 23, 20, 26 ], 
  [ 11, 17, 14, 16, 13, 10, 15, 12, 18, 8, 5, 2, 4, 1, 7, 3, 9, 6, 23, 20, 26, 19, 25, 22, 27, 24, 21 ], 
  [ 15, 12, 18, 11, 17, 14, 16, 13, 10, 3, 9, 6, 8, 5, 2, 4, 1, 7, 27, 24, 21, 23, 20, 26, 19, 25, 22 ], 
  [ 14, 11, 17, 10, 16, 13, 18, 15, 12, 2, 8, 5, 7, 4, 1, 6, 3, 9, 26, 23, 20, 22, 19, 25, 21, 27, 24 ], 
  [ 18, 15, 12, 14, 11, 17, 10, 16, 13, 6, 3, 9, 2, 8, 5, 7, 4, 1, 21, 27, 24, 26, 23, 20, 22, 19, 25 ], 
  [ 10, 16, 13, 18, 15, 12, 14, 11, 17, 7, 4, 1, 6, 3, 9, 2, 8, 5, 22, 19, 25, 21, 27, 24, 26, 23, 20 ], 
  [ 12, 18, 15, 17, 14, 11, 13, 10, 16, 9, 6, 3, 5, 2, 8, 1, 7, 4, 24, 21, 27, 20, 26, 23, 25, 22, 19 ], 
  [ 13, 10, 16, 12, 18, 15, 17, 14, 11, 1, 7, 4, 9, 6, 3, 5, 2, 8, 25, 22, 19, 24, 21, 27, 20, 26, 23 ], 
  [ 17, 14, 11, 13, 10, 16, 12, 18, 15, 5, 2, 8, 1, 7, 4, 9, 6, 3, 20, 26, 23, 25, 22, 19, 24, 21, 27 ] ]);
QUANDLES[27].implemented := 30;
QUANDLES[27].rack[30] := rec( size := 27, matrix :=
[ [ 1, 4, 7, 5, 8, 2, 9, 3, 6, 21, 24, 27, 22, 25, 19, 26, 20, 23, 11, 14, 17, 15, 18, 12, 16, 10, 13 ], 
  [ 8, 2, 5, 3, 6, 9, 4, 7, 1, 25, 19, 22, 20, 23, 26, 24, 27, 21, 18, 12, 15, 10, 13, 16, 14, 17, 11 ], 
  [ 6, 9, 3, 7, 1, 4, 2, 5, 8, 23, 26, 20, 27, 21, 24, 19, 22, 25, 13, 16, 10, 17, 11, 14, 12, 15, 18 ], 
  [ 3, 6, 9, 4, 7, 1, 8, 2, 5, 20, 23, 26, 24, 27, 21, 25, 19, 22, 10, 13, 16, 14, 17, 11, 18, 12, 15 ], 
  [ 7, 1, 4, 2, 5, 8, 6, 9, 3, 27, 21, 24, 19, 22, 25, 23, 26, 20, 17, 11, 14, 12, 15, 18, 13, 16, 10 ], 
  [ 5, 8, 2, 9, 3, 6, 1, 4, 7, 22, 25, 19, 26, 20, 23, 21, 24, 27, 15, 18, 12, 16, 10, 13, 11, 14, 17 ], 
  [ 2, 5, 8, 6, 9, 3, 7, 1, 4, 19, 22, 25, 23, 26, 20, 27, 21, 24, 12, 15, 18, 13, 16, 10, 17, 11, 14 ], 
  [ 9, 3, 6, 1, 4, 7, 5, 8, 2, 26, 20, 23, 21, 24, 27, 22, 25, 19, 16, 10, 13, 11, 14, 17, 15, 18, 12 ], 
  [ 4, 7, 1, 8, 2, 5, 3, 6, 9, 24, 27, 21, 25, 19, 22, 20, 23, 26, 14, 17, 11, 18, 12, 15, 10, 13, 16 ], 
  [ 20, 23, 26, 24, 27, 21, 25, 19, 22, 10, 13, 16, 14, 17, 11, 18, 12, 15, 3, 6, 9, 4, 7, 1, 8, 2, 5 ], 
  [ 27, 21, 24, 19, 22, 25, 23, 26, 20, 17, 11, 14, 12, 15, 18, 13, 16, 10, 7, 1, 4, 2, 5, 8, 6, 9, 3 ], 
  [ 22, 25, 19, 26, 20, 23, 21, 24, 27, 15, 18, 12, 16, 10, 13, 11, 14, 17, 5, 8, 2, 9, 3, 6, 1, 4, 7 ], 
  [ 19, 22, 25, 23, 26, 20, 27, 21, 24, 12, 15, 18, 13, 16, 10, 17, 11, 14, 2, 5, 8, 6, 9, 3, 7, 1, 4 ], 
  [ 26, 20, 23, 21, 24, 27, 22, 25, 19, 16, 10, 13, 11, 14, 17, 15, 18, 12, 9, 3, 6, 1, 4, 7, 5, 8, 2 ], 
  [ 24, 27, 21, 25, 19, 22, 20, 23, 26, 14, 17, 11, 18, 12, 15, 10, 13, 16, 4, 7, 1, 8, 2, 5, 3, 6, 9 ], 
  [ 21, 24, 27, 22, 25, 19, 26, 20, 23, 11, 14, 17, 15, 18, 12, 16, 10, 13, 1, 4, 7, 5, 8, 2, 9, 3, 6 ], 
  [ 25, 19, 22, 20, 23, 26, 24, 27, 21, 18, 12, 15, 10, 13, 16, 14, 17, 11, 8, 2, 5, 3, 6, 9, 4, 7, 1 ], 
  [ 23, 26, 20, 27, 21, 24, 19, 22, 25, 13, 16, 10, 17, 11, 14, 12, 15, 18, 6, 9, 3, 7, 1, 4, 2, 5, 8 ], 
  [ 12, 15, 18, 13, 16, 10, 17, 11, 14, 2, 5, 8, 6, 9, 3, 7, 1, 4, 19, 22, 25, 23, 26, 20, 27, 21, 24 ], 
  [ 16, 10, 13, 11, 14, 17, 15, 18, 12, 9, 3, 6, 1, 4, 7, 5, 8, 2, 26, 20, 23, 21, 24, 27, 22, 25, 19 ], 
  [ 14, 17, 11, 18, 12, 15, 10, 13, 16, 4, 7, 1, 8, 2, 5, 3, 6, 9, 24, 27, 21, 25, 19, 22, 20, 23, 26 ], 
  [ 11, 14, 17, 15, 18, 12, 16, 10, 13, 1, 4, 7, 5, 8, 2, 9, 3, 6, 21, 24, 27, 22, 25, 19, 26, 20, 23 ], 
  [ 18, 12, 15, 10, 13, 16, 14, 17, 11, 8, 2, 5, 3, 6, 9, 4, 7, 1, 25, 19, 22, 20, 23, 26, 24, 27, 21 ], 
  [ 13, 16, 10, 17, 11, 14, 12, 15, 18, 6, 9, 3, 7, 1, 4, 2, 5, 8, 23, 26, 20, 27, 21, 24, 19, 22, 25 ], 
  [ 10, 13, 16, 14, 17, 11, 18, 12, 15, 3, 6, 9, 4, 7, 1, 8, 2, 5, 20, 23, 26, 24, 27, 21, 25, 19, 22 ], 
  [ 17, 11, 14, 12, 15, 18, 13, 16, 10, 7, 1, 4, 2, 5, 8, 6, 9, 3, 27, 21, 24, 19, 22, 25, 23, 26, 20 ], 
  [ 15, 18, 12, 16, 10, 13, 11, 14, 17, 5, 8, 2, 9, 3, 6, 1, 4, 7, 22, 25, 19, 26, 20, 23, 21, 24, 27 ] ]);
QUANDLES[27].implemented := 31;
QUANDLES[27].rack[31] := rec( size := 27, matrix :=
[ [ 1, 18, 23, 2, 16, 24, 3, 17, 22, 4, 12, 26, 5, 10, 27, 6, 11, 25, 7, 15, 20, 8, 13, 21, 9, 14, 19 ], 
  [ 24, 2, 16, 22, 3, 17, 23, 1, 18, 27, 5, 10, 25, 6, 11, 26, 4, 12, 21, 8, 13, 19, 9, 14, 20, 7, 15 ], 
  [ 17, 22, 3, 18, 23, 1, 16, 24, 2, 11, 25, 6, 12, 26, 4, 10, 27, 5, 14, 19, 9, 15, 20, 7, 13, 21, 8 ], 
  [ 6, 11, 25, 4, 12, 26, 5, 10, 27, 9, 14, 19, 7, 15, 20, 8, 13, 21, 3, 17, 22, 1, 18, 23, 2, 16, 24 ], 
  [ 26, 4, 12, 27, 5, 10, 25, 6, 11, 20, 7, 15, 21, 8, 13, 19, 9, 14, 23, 1, 18, 24, 2, 16, 22, 3, 17 ], 
  [ 10, 27, 5, 11, 25, 6, 12, 26, 4, 13, 21, 8, 14, 19, 9, 15, 20, 7, 16, 24, 2, 17, 22, 3, 18, 23, 1 ], 
  [ 8, 13, 21, 9, 14, 19, 7, 15, 20, 2, 16, 24, 3, 17, 22, 1, 18, 23, 5, 10, 27, 6, 11, 25, 4, 12, 26 ], 
  [ 19, 9, 14, 20, 7, 15, 21, 8, 13, 22, 3, 17, 23, 1, 18, 24, 2, 16, 25, 6, 11, 26, 4, 12, 27, 5, 10 ], 
  [ 15, 20, 7, 13, 21, 8, 14, 19, 9, 18, 23, 1, 16, 24, 2, 17, 22, 3, 12, 26, 4, 10, 27, 5, 11, 25, 6 ], 
  [ 16, 24, 2, 17, 22, 3, 18, 23, 1, 10, 27, 5, 11, 25, 6, 12, 26, 4, 13, 21, 8, 14, 19, 9, 15, 20, 7 ], 
  [ 3, 17, 22, 1, 18, 23, 2, 16, 24, 6, 11, 25, 4, 12, 26, 5, 10, 27, 9, 14, 19, 7, 15, 20, 8, 13, 21 ], 
  [ 23, 1, 18, 24, 2, 16, 22, 3, 17, 26, 4, 12, 27, 5, 10, 25, 6, 11, 20, 7, 15, 21, 8, 13, 19, 9, 14 ], 
  [ 12, 26, 4, 10, 27, 5, 11, 25, 6, 15, 20, 7, 13, 21, 8, 14, 19, 9, 18, 23, 1, 16, 24, 2, 17, 22, 3 ], 
  [ 5, 10, 27, 6, 11, 25, 4, 12, 26, 8, 13, 21, 9, 14, 19, 7, 15, 20, 2, 16, 24, 3, 17, 22, 1, 18, 23 ], 
  [ 25, 6, 11, 26, 4, 12, 27, 5, 10, 19, 9, 14, 20, 7, 15, 21, 8, 13, 22, 3, 17, 23, 1, 18, 24, 2, 16 ], 
  [ 14, 19, 9, 15, 20, 7, 13, 21, 8, 17, 22, 3, 18, 23, 1, 16, 24, 2, 11, 25, 6, 12, 26, 4, 10, 27, 5 ], 
  [ 7, 15, 20, 8, 13, 21, 9, 14, 19, 1, 18, 23, 2, 16, 24, 3, 17, 22, 4, 12, 26, 5, 10, 27, 6, 11, 25 ], 
  [ 21, 8, 13, 19, 9, 14, 20, 7, 15, 24, 2, 16, 22, 3, 17, 23, 1, 18, 27, 5, 10, 25, 6, 11, 26, 4, 12 ], 
  [ 22, 3, 17, 23, 1, 18, 24, 2, 16, 25, 6, 11, 26, 4, 12, 27, 5, 10, 19, 9, 14, 20, 7, 15, 21, 8, 13 ], 
  [ 18, 23, 1, 16, 24, 2, 17, 22, 3, 12, 26, 4, 10, 27, 5, 11, 25, 6, 15, 20, 7, 13, 21, 8, 14, 19, 9 ], 
  [ 2, 16, 24, 3, 17, 22, 1, 18, 23, 5, 10, 27, 6, 11, 25, 4, 12, 26, 8, 13, 21, 9, 14, 19, 7, 15, 20 ], 
  [ 27, 5, 10, 25, 6, 11, 26, 4, 12, 21, 8, 13, 19, 9, 14, 20, 7, 15, 24, 2, 16, 22, 3, 17, 23, 1, 18 ], 
  [ 11, 25, 6, 12, 26, 4, 10, 27, 5, 14, 19, 9, 15, 20, 7, 13, 21, 8, 17, 22, 3, 18, 23, 1, 16, 24, 2 ], 
  [ 4, 12, 26, 5, 10, 27, 6, 11, 25, 7, 15, 20, 8, 13, 21, 9, 14, 19, 1, 18, 23, 2, 16, 24, 3, 17, 22 ], 
  [ 20, 7, 15, 21, 8, 13, 19, 9, 14, 23, 1, 18, 24, 2, 16, 22, 3, 17, 26, 4, 12, 27, 5, 10, 25, 6, 11 ], 
  [ 13, 21, 8, 14, 19, 9, 15, 20, 7, 16, 24, 2, 17, 22, 3, 18, 23, 1, 10, 27, 5, 11, 25, 6, 12, 26, 4 ], 
  [ 9, 14, 19, 7, 15, 20, 8, 13, 21, 3, 17, 22, 1, 18, 23, 2, 16, 24, 6, 11, 25, 4, 12, 26, 5, 10, 27 ] ]);
QUANDLES[27].implemented := 32;
QUANDLES[27].rack[32] := rec( size := 27, matrix :=
[ [ 1, 25, 13, 18, 6, 21, 23, 11, 8, 2, 26, 14, 16, 4, 19, 24, 12, 9, 3, 27, 15, 17, 5, 20, 22, 10, 7 ], 
  [ 14, 2, 26, 19, 16, 4, 9, 24, 12, 15, 3, 27, 20, 17, 5, 7, 22, 10, 13, 1, 25, 21, 18, 6, 8, 23, 11 ], 
  [ 27, 15, 3, 5, 20, 17, 10, 7, 22, 25, 13, 1, 6, 21, 18, 11, 8, 23, 26, 14, 2, 4, 19, 16, 12, 9, 24 ], 
  [ 26, 14, 2, 4, 19, 16, 12, 9, 24, 27, 15, 3, 5, 20, 17, 10, 7, 22, 25, 13, 1, 6, 21, 18, 11, 8, 23 ], 
  [ 3, 27, 15, 17, 5, 20, 22, 10, 7, 1, 25, 13, 18, 6, 21, 23, 11, 8, 2, 26, 14, 16, 4, 19, 24, 12, 9 ], 
  [ 13, 1, 25, 21, 18, 6, 8, 23, 11, 14, 2, 26, 19, 16, 4, 9, 24, 12, 15, 3, 27, 20, 17, 5, 7, 22, 10 ], 
  [ 15, 3, 27, 20, 17, 5, 7, 22, 10, 13, 1, 25, 21, 18, 6, 8, 23, 11, 14, 2, 26, 19, 16, 4, 9, 24, 12 ], 
  [ 25, 13, 1, 6, 21, 18, 11, 8, 23, 26, 14, 2, 4, 19, 16, 12, 9, 24, 27, 15, 3, 5, 20, 17, 10, 7, 22 ], 
  [ 2, 26, 14, 16, 4, 19, 24, 12, 9, 3, 27, 15, 17, 5, 20, 22, 10, 7, 1, 25, 13, 18, 6, 21, 23, 11, 8 ], 
  [ 12, 9, 24, 26, 14, 2, 4, 19, 16, 10, 7, 22, 27, 15, 3, 5, 20, 17, 11, 8, 23, 25, 13, 1, 6, 21, 18 ], 
  [ 22, 10, 7, 3, 27, 15, 17, 5, 20, 23, 11, 8, 1, 25, 13, 18, 6, 21, 24, 12, 9, 2, 26, 14, 16, 4, 19 ], 
  [ 8, 23, 11, 13, 1, 25, 21, 18, 6, 9, 24, 12, 14, 2, 26, 19, 16, 4, 7, 22, 10, 15, 3, 27, 20, 17, 5 ], 
  [ 7, 22, 10, 15, 3, 27, 20, 17, 5, 8, 23, 11, 13, 1, 25, 21, 18, 6, 9, 24, 12, 14, 2, 26, 19, 16, 4 ], 
  [ 11, 8, 23, 25, 13, 1, 6, 21, 18, 12, 9, 24, 26, 14, 2, 4, 19, 16, 10, 7, 22, 27, 15, 3, 5, 20, 17 ], 
  [ 24, 12, 9, 2, 26, 14, 16, 4, 19, 22, 10, 7, 3, 27, 15, 17, 5, 20, 23, 11, 8, 1, 25, 13, 18, 6, 21 ], 
  [ 23, 11, 8, 1, 25, 13, 18, 6, 21, 24, 12, 9, 2, 26, 14, 16, 4, 19, 22, 10, 7, 3, 27, 15, 17, 5, 20 ], 
  [ 9, 24, 12, 14, 2, 26, 19, 16, 4, 7, 22, 10, 15, 3, 27, 20, 17, 5, 8, 23, 11, 13, 1, 25, 21, 18, 6 ], 
  [ 10, 7, 22, 27, 15, 3, 5, 20, 17, 11, 8, 23, 25, 13, 1, 6, 21, 18, 12, 9, 24, 26, 14, 2, 4, 19, 16 ], 
  [ 20, 17, 5, 7, 22, 10, 15, 3, 27, 21, 18, 6, 8, 23, 11, 13, 1, 25, 19, 16, 4, 9, 24, 12, 14, 2, 26 ], 
  [ 6, 21, 18, 11, 8, 23, 25, 13, 1, 4, 19, 16, 12, 9, 24, 26, 14, 2, 5, 20, 17, 10, 7, 22, 27, 15, 3 ], 
  [ 16, 4, 19, 24, 12, 9, 2, 26, 14, 17, 5, 20, 22, 10, 7, 3, 27, 15, 18, 6, 21, 23, 11, 8, 1, 25, 13 ], 
  [ 18, 6, 21, 23, 11, 8, 1, 25, 13, 16, 4, 19, 24, 12, 9, 2, 26, 14, 17, 5, 20, 22, 10, 7, 3, 27, 15 ], 
  [ 19, 16, 4, 9, 24, 12, 14, 2, 26, 20, 17, 5, 7, 22, 10, 15, 3, 27, 21, 18, 6, 8, 23, 11, 13, 1, 25 ], 
  [ 5, 20, 17, 10, 7, 22, 27, 15, 3, 6, 21, 18, 11, 8, 23, 25, 13, 1, 4, 19, 16, 12, 9, 24, 26, 14, 2 ], 
  [ 4, 19, 16, 12, 9, 24, 26, 14, 2, 5, 20, 17, 10, 7, 22, 27, 15, 3, 6, 21, 18, 11, 8, 23, 25, 13, 1 ], 
  [ 17, 5, 20, 22, 10, 7, 3, 27, 15, 18, 6, 21, 23, 11, 8, 1, 25, 13, 16, 4, 19, 24, 12, 9, 2, 26, 14 ], 
  [ 21, 18, 6, 8, 23, 11, 13, 1, 25, 19, 16, 4, 9, 24, 12, 14, 2, 26, 20, 17, 5, 7, 22, 10, 15, 3, 27 ] ]);
QUANDLES[27].implemented := 33;
QUANDLES[27].rack[33] := rec( size := 27, matrix :=
[ [ 1, 22, 16, 9, 21, 15, 5, 26, 11, 25, 10, 4, 24, 18, 3, 20, 14, 8, 13, 7, 19, 12, 6, 27, 17, 2, 23 ], 
  [ 17, 2, 23, 13, 7, 19, 12, 6, 27, 5, 26, 11, 1, 22, 16, 9, 21, 15, 20, 14, 8, 25, 10, 4, 24, 18, 3 ], 
  [ 24, 18, 3, 20, 14, 8, 25, 10, 4, 12, 6, 27, 17, 2, 23, 13, 7, 19, 9, 21, 15, 5, 26, 11, 1, 22, 16 ], 
  [ 8, 20, 14, 4, 25, 10, 3, 24, 18, 23, 17, 2, 19, 13, 7, 27, 12, 6, 11, 5, 26, 16, 1, 22, 15, 9, 21 ], 
  [ 15, 9, 21, 11, 5, 26, 16, 1, 22, 3, 24, 18, 8, 20, 14, 4, 25, 10, 27, 12, 6, 23, 17, 2, 19, 13, 7 ], 
  [ 19, 13, 7, 27, 12, 6, 23, 17, 2, 16, 1, 22, 15, 9, 21, 11, 5, 26, 4, 25, 10, 3, 24, 18, 8, 20, 14 ], 
  [ 6, 27, 12, 2, 23, 17, 7, 19, 13, 21, 15, 9, 26, 11, 5, 22, 16, 1, 18, 3, 24, 14, 8, 20, 10, 4, 25 ], 
  [ 10, 4, 25, 18, 3, 24, 14, 8, 20, 7, 19, 13, 6, 27, 12, 2, 23, 17, 22, 16, 1, 21, 15, 9, 26, 11, 5 ], 
  [ 26, 11, 5, 22, 16, 1, 21, 15, 9, 14, 8, 20, 10, 4, 25, 18, 3, 24, 2, 23, 17, 7, 19, 13, 6, 27, 12 ], 
  [ 22, 16, 1, 21, 15, 9, 26, 11, 5, 10, 4, 25, 18, 3, 24, 14, 8, 20, 7, 19, 13, 6, 27, 12, 2, 23, 17 ], 
  [ 2, 23, 17, 7, 19, 13, 6, 27, 12, 26, 11, 5, 22, 16, 1, 21, 15, 9, 14, 8, 20, 10, 4, 25, 18, 3, 24 ], 
  [ 18, 3, 24, 14, 8, 20, 10, 4, 25, 6, 27, 12, 2, 23, 17, 7, 19, 13, 21, 15, 9, 26, 11, 5, 22, 16, 1 ], 
  [ 20, 14, 8, 25, 10, 4, 24, 18, 3, 17, 2, 23, 13, 7, 19, 12, 6, 27, 5, 26, 11, 1, 22, 16, 9, 21, 15 ], 
  [ 9, 21, 15, 5, 26, 11, 1, 22, 16, 24, 18, 3, 20, 14, 8, 25, 10, 4, 12, 6, 27, 17, 2, 23, 13, 7, 19 ], 
  [ 13, 7, 19, 12, 6, 27, 17, 2, 23, 1, 22, 16, 9, 21, 15, 5, 26, 11, 25, 10, 4, 24, 18, 3, 20, 14, 8 ], 
  [ 27, 12, 6, 23, 17, 2, 19, 13, 7, 15, 9, 21, 11, 5, 26, 16, 1, 22, 3, 24, 18, 8, 20, 14, 4, 25, 10 ], 
  [ 4, 25, 10, 3, 24, 18, 8, 20, 14, 19, 13, 7, 27, 12, 6, 23, 17, 2, 16, 1, 22, 15, 9, 21, 11, 5, 26 ], 
  [ 11, 5, 26, 16, 1, 22, 15, 9, 21, 8, 20, 14, 4, 25, 10, 3, 24, 18, 23, 17, 2, 19, 13, 7, 27, 12, 6 ], 
  [ 16, 1, 22, 15, 9, 21, 11, 5, 26, 4, 25, 10, 3, 24, 18, 8, 20, 14, 19, 13, 7, 27, 12, 6, 23, 17, 2 ], 
  [ 23, 17, 2, 19, 13, 7, 27, 12, 6, 11, 5, 26, 16, 1, 22, 15, 9, 21, 8, 20, 14, 4, 25, 10, 3, 24, 18 ], 
  [ 3, 24, 18, 8, 20, 14, 4, 25, 10, 27, 12, 6, 23, 17, 2, 19, 13, 7, 15, 9, 21, 11, 5, 26, 16, 1, 22 ], 
  [ 14, 8, 20, 10, 4, 25, 18, 3, 24, 2, 23, 17, 7, 19, 13, 6, 27, 12, 26, 11, 5, 22, 16, 1, 21, 15, 9 ], 
  [ 21, 15, 9, 26, 11, 5, 22, 16, 1, 18, 3, 24, 14, 8, 20, 10, 4, 25, 6, 27, 12, 2, 23, 17, 7, 19, 13 ], 
  [ 7, 19, 13, 6, 27, 12, 2, 23, 17, 22, 16, 1, 21, 15, 9, 26, 11, 5, 10, 4, 25, 18, 3, 24, 14, 8, 20 ], 
  [ 12, 6, 27, 17, 2, 23, 13, 7, 19, 9, 21, 15, 5, 26, 11, 1, 22, 16, 24, 18, 3, 20, 14, 8, 25, 10, 4 ], 
  [ 25, 10, 4, 24, 18, 3, 20, 14, 8, 13, 7, 19, 12, 6, 27, 17, 2, 23, 1, 22, 16, 9, 21, 15, 5, 26, 11 ], 
  [ 5, 26, 11, 1, 22, 16, 9, 21, 15, 20, 14, 8, 25, 10, 4, 24, 18, 3, 17, 2, 23, 13, 7, 19, 12, 6, 27 ] ]);
QUANDLES[27].implemented := 34;
QUANDLES[27].rack[34] := rec( size := 27, matrix :=
[ [ 1, 11, 21, 17, 27, 7, 24, 4, 14, 8, 18, 25, 15, 22, 5, 19, 2, 12, 6, 13, 23, 10, 20, 3, 26, 9, 16 ], 
  [ 19, 2, 12, 8, 18, 25, 15, 22, 5, 26, 9, 16, 6, 13, 23, 10, 20, 3, 24, 4, 14, 1, 11, 21, 17, 27, 7 ], 
  [ 10, 20, 3, 26, 9, 16, 6, 13, 23, 17, 27, 7, 24, 4, 14, 1, 11, 21, 15, 22, 5, 19, 2, 12, 8, 18, 25 ], 
  [ 27, 7, 17, 4, 14, 24, 11, 21, 1, 22, 5, 15, 2, 12, 19, 18, 25, 8, 20, 3, 10, 9, 16, 26, 13, 23, 6 ], 
  [ 18, 25, 8, 22, 5, 15, 2, 12, 19, 13, 23, 6, 20, 3, 10, 9, 16, 26, 11, 21, 1, 27, 7, 17, 4, 14, 24 ], 
  [ 9, 16, 26, 13, 23, 6, 20, 3, 10, 4, 14, 24, 11, 21, 1, 27, 7, 17, 2, 12, 19, 18, 25, 8, 22, 5, 15 ], 
  [ 14, 24, 4, 21, 1, 11, 7, 17, 27, 12, 19, 2, 25, 8, 18, 5, 15, 22, 16, 26, 9, 23, 6, 13, 3, 10, 20 ], 
  [ 5, 15, 22, 12, 19, 2, 25, 8, 18, 3, 10, 20, 16, 26, 9, 23, 6, 13, 7, 17, 27, 14, 24, 4, 21, 1, 11 ], 
  [ 23, 6, 13, 3, 10, 20, 16, 26, 9, 21, 1, 11, 7, 17, 27, 14, 24, 4, 25, 8, 18, 5, 15, 22, 12, 19, 2 ], 
  [ 15, 22, 5, 19, 2, 12, 8, 18, 25, 10, 20, 3, 26, 9, 16, 6, 13, 23, 17, 27, 7, 24, 4, 14, 1, 11, 21 ], 
  [ 6, 13, 23, 10, 20, 3, 26, 9, 16, 1, 11, 21, 17, 27, 7, 24, 4, 14, 8, 18, 25, 15, 22, 5, 19, 2, 12 ], 
  [ 24, 4, 14, 1, 11, 21, 17, 27, 7, 19, 2, 12, 8, 18, 25, 15, 22, 5, 26, 9, 16, 6, 13, 23, 10, 20, 3 ], 
  [ 2, 12, 19, 18, 25, 8, 22, 5, 15, 9, 16, 26, 13, 23, 6, 20, 3, 10, 4, 14, 24, 11, 21, 1, 27, 7, 17 ], 
  [ 20, 3, 10, 9, 16, 26, 13, 23, 6, 27, 7, 17, 4, 14, 24, 11, 21, 1, 22, 5, 15, 2, 12, 19, 18, 25, 8 ], 
  [ 11, 21, 1, 27, 7, 17, 4, 14, 24, 18, 25, 8, 22, 5, 15, 2, 12, 19, 13, 23, 6, 20, 3, 10, 9, 16, 26 ], 
  [ 25, 8, 18, 5, 15, 22, 12, 19, 2, 23, 6, 13, 3, 10, 20, 16, 26, 9, 21, 1, 11, 7, 17, 27, 14, 24, 4 ], 
  [ 16, 26, 9, 23, 6, 13, 3, 10, 20, 14, 24, 4, 21, 1, 11, 7, 17, 27, 12, 19, 2, 25, 8, 18, 5, 15, 22 ], 
  [ 7, 17, 27, 14, 24, 4, 21, 1, 11, 5, 15, 22, 12, 19, 2, 25, 8, 18, 3, 10, 20, 16, 26, 9, 23, 6, 13 ], 
  [ 26, 9, 16, 6, 13, 23, 10, 20, 3, 24, 4, 14, 1, 11, 21, 17, 27, 7, 19, 2, 12, 8, 18, 25, 15, 22, 5 ], 
  [ 17, 27, 7, 24, 4, 14, 1, 11, 21, 15, 22, 5, 19, 2, 12, 8, 18, 25, 10, 20, 3, 26, 9, 16, 6, 13, 23 ], 
  [ 8, 18, 25, 15, 22, 5, 19, 2, 12, 6, 13, 23, 10, 20, 3, 26, 9, 16, 1, 11, 21, 17, 27, 7, 24, 4, 14 ], 
  [ 13, 23, 6, 20, 3, 10, 9, 16, 26, 11, 21, 1, 27, 7, 17, 4, 14, 24, 18, 25, 8, 22, 5, 15, 2, 12, 19 ], 
  [ 4, 14, 24, 11, 21, 1, 27, 7, 17, 2, 12, 19, 18, 25, 8, 22, 5, 15, 9, 16, 26, 13, 23, 6, 20, 3, 10 ], 
  [ 22, 5, 15, 2, 12, 19, 18, 25, 8, 20, 3, 10, 9, 16, 26, 13, 23, 6, 27, 7, 17, 4, 14, 24, 11, 21, 1 ], 
  [ 3, 10, 20, 16, 26, 9, 23, 6, 13, 7, 17, 27, 14, 24, 4, 21, 1, 11, 5, 15, 22, 12, 19, 2, 25, 8, 18 ], 
  [ 21, 1, 11, 7, 17, 27, 14, 24, 4, 25, 8, 18, 5, 15, 22, 12, 19, 2, 23, 6, 13, 3, 10, 20, 16, 26, 9 ], 
  [ 12, 19, 2, 25, 8, 18, 5, 15, 22, 16, 26, 9, 23, 6, 13, 3, 10, 20, 14, 24, 4, 21, 1, 11, 7, 17, 27 ] ]);
QUANDLES[27].implemented := 35;
QUANDLES[27].rack[35] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 9, 8, 7, 4, 6, 5, 2, 1, 3, 26, 25, 27, 24, 23, 22, 19, 21, 20, 18, 17, 16, 13, 15, 14, 11, 10, 12 ], 
  [ 8, 7, 9, 6, 5, 4, 1, 3, 2, 25, 27, 26, 23, 22, 24, 21, 20, 19, 17, 16, 18, 15, 14, 13, 10, 12, 11 ], 
  [ 7, 9, 8, 5, 4, 6, 3, 2, 1, 27, 26, 25, 22, 24, 23, 20, 19, 21, 16, 18, 17, 14, 13, 15, 12, 11, 10 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 23, 22, 24, 19, 21, 20, 27, 26, 25, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 22, 24, 23, 21, 20, 19, 26, 25, 27, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 24, 23, 22, 20, 19, 21, 25, 27, 26, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 10, 12, 11, 17, 16, 18, 15, 14, 13, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 12, 11, 10, 16, 18, 17, 14, 13, 15, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 11, 10, 12, 18, 17, 16, 13, 15, 14, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 26, 25, 27, 24, 23, 22, 19, 21, 20, 18, 17, 16, 13, 15, 14, 11, 10, 12, 7, 9, 8, 5, 4, 6, 3, 2, 1 ], 
  [ 25, 27, 26, 23, 22, 24, 21, 20, 19, 17, 16, 18, 15, 14, 13, 10, 12, 11, 9, 8, 7, 4, 6, 5, 2, 1, 3 ], 
  [ 27, 26, 25, 22, 24, 23, 20, 19, 21, 16, 18, 17, 14, 13, 15, 12, 11, 10, 8, 7, 9, 6, 5, 4, 1, 3, 2 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 14, 13, 15, 12, 11, 10, 16, 18, 17, 4, 6, 5, 3, 2, 1, 8, 7, 9 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 13, 15, 14, 11, 10, 12, 18, 17, 16, 6, 5, 4, 2, 1, 3, 7, 9, 8 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 15, 14, 13, 10, 12, 11, 17, 16, 18, 5, 4, 6, 1, 3, 2, 9, 8, 7 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 2, 1, 3, 7, 9, 8, 6, 5, 4, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 1, 3, 2, 9, 8, 7, 5, 4, 6, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 3, 2, 1, 8, 7, 9, 4, 6, 5, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 18, 17, 16, 13, 15, 14, 11, 10, 12, 7, 9, 8, 5, 4, 6, 3, 2, 1, 27, 26, 25, 22, 24, 23, 20, 19, 21 ], 
  [ 17, 16, 18, 15, 14, 13, 10, 12, 11, 9, 8, 7, 4, 6, 5, 2, 1, 3, 26, 25, 27, 24, 23, 22, 19, 21, 20 ], 
  [ 16, 18, 17, 14, 13, 15, 12, 11, 10, 8, 7, 9, 6, 5, 4, 1, 3, 2, 25, 27, 26, 23, 22, 24, 21, 20, 19 ], 
  [ 15, 14, 13, 11, 10, 12, 16, 18, 17, 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 14, 13, 15, 10, 12, 11, 18, 17, 16, 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 13, 15, 14, 12, 11, 10, 17, 16, 18, 6, 5, 4, 3, 2, 1, 9, 8, 7, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 36;
QUANDLES[27].rack[36] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 19, 21, 20, 25, 27, 26, 22, 24, 23, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 21, 20, 19, 27, 26, 25, 24, 23, 22, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 20, 19, 21, 26, 25, 27, 23, 22, 24, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 2, 1, 3, 27, 26, 25, 22, 24, 23, 20, 19, 21, 17, 16, 18, 15, 14, 13, 10, 12, 11 ], 
  [ 8, 7, 9, 6, 5, 4, 1, 3, 2, 26, 25, 27, 24, 23, 22, 19, 21, 20, 16, 18, 17, 14, 13, 15, 12, 11, 10 ], 
  [ 7, 9, 8, 5, 4, 6, 3, 2, 1, 25, 27, 26, 23, 22, 24, 21, 20, 19, 18, 17, 16, 13, 15, 14, 11, 10, 12 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 24, 23, 22, 20, 19, 21, 25, 27, 26, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 23, 22, 24, 19, 21, 20, 27, 26, 25, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 22, 24, 23, 21, 20, 19, 26, 25, 27, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 10, 12, 11, 17, 16, 18, 15, 14, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 12, 11, 10, 16, 18, 17, 14, 13, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 11, 10, 12, 18, 17, 16, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 25, 27, 26, 23, 22, 24, 21, 20, 19, 18, 17, 16, 13, 15, 14, 11, 10, 12, 8, 7, 9, 6, 5, 4, 1, 3, 2 ], 
  [ 27, 26, 25, 22, 24, 23, 20, 19, 21, 17, 16, 18, 15, 14, 13, 10, 12, 11, 7, 9, 8, 5, 4, 6, 3, 2, 1 ], 
  [ 26, 25, 27, 24, 23, 22, 19, 21, 20, 16, 18, 17, 14, 13, 15, 12, 11, 10, 9, 8, 7, 4, 6, 5, 2, 1, 3 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 13, 15, 12, 11, 10, 16, 18, 17, 5, 4, 6, 1, 3, 2, 9, 8, 7 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 15, 14, 11, 10, 12, 18, 17, 16, 4, 6, 5, 3, 2, 1, 8, 7, 9 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 15, 14, 13, 10, 12, 11, 17, 16, 18, 6, 5, 4, 2, 1, 3, 7, 9, 8 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 1, 3, 2, 9, 8, 7, 5, 4, 6, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 3, 2, 1, 8, 7, 9, 4, 6, 5, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 2, 1, 3, 7, 9, 8, 6, 5, 4, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 16, 18, 17, 14, 13, 15, 12, 11, 10, 9, 8, 7, 4, 6, 5, 2, 1, 3, 27, 26, 25, 22, 24, 23, 20, 19, 21 ], 
  [ 18, 17, 16, 13, 15, 14, 11, 10, 12, 8, 7, 9, 6, 5, 4, 1, 3, 2, 26, 25, 27, 24, 23, 22, 19, 21, 20 ], 
  [ 17, 16, 18, 15, 14, 13, 10, 12, 11, 7, 9, 8, 5, 4, 6, 3, 2, 1, 25, 27, 26, 23, 22, 24, 21, 20, 19 ], 
  [ 13, 15, 14, 12, 11, 10, 17, 16, 18, 4, 6, 5, 1, 3, 2, 7, 9, 8, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 15, 14, 13, 11, 10, 12, 16, 18, 17, 6, 5, 4, 3, 2, 1, 9, 8, 7, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 14, 13, 15, 10, 12, 11, 18, 17, 16, 5, 4, 6, 2, 1, 3, 8, 7, 9, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 37;
QUANDLES[27].rack[37] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 4, 6, 5, 26, 25, 27, 22, 24, 23, 19, 21, 20, 14, 13, 15, 12, 11, 10, 16, 18, 17 ], 
  [ 3, 2, 1, 8, 7, 9, 6, 5, 4, 25, 27, 26, 24, 23, 22, 21, 20, 19, 13, 15, 14, 11, 10, 12, 18, 17, 16 ], 
  [ 2, 1, 3, 7, 9, 8, 5, 4, 6, 27, 26, 25, 23, 22, 24, 20, 19, 21, 15, 14, 13, 10, 12, 11, 17, 16, 18 ], 
  [ 8, 7, 9, 4, 6, 5, 1, 3, 2, 23, 22, 24, 21, 20, 19, 25, 27, 26, 10, 12, 11, 18, 17, 16, 13, 15, 14 ], 
  [ 7, 9, 8, 6, 5, 4, 3, 2, 1, 22, 24, 23, 20, 19, 21, 27, 26, 25, 12, 11, 10, 17, 16, 18, 15, 14, 13 ], 
  [ 9, 8, 7, 5, 4, 6, 2, 1, 3, 24, 23, 22, 19, 21, 20, 26, 25, 27, 11, 10, 12, 16, 18, 17, 14, 13, 15 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 21, 20, 19, 26, 25, 27, 24, 23, 22, 18, 17, 16, 14, 13, 15, 11, 10, 12 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 20, 19, 21, 25, 27, 26, 23, 22, 24, 17, 16, 18, 13, 15, 14, 10, 12, 11 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 19, 21, 20, 27, 26, 25, 22, 24, 23, 16, 18, 17, 15, 14, 13, 12, 11, 10 ], 
  [ 24, 23, 22, 19, 21, 20, 26, 25, 27, 10, 12, 11, 18, 17, 16, 13, 15, 14, 9, 8, 7, 5, 4, 6, 2, 1, 3 ], 
  [ 23, 22, 24, 21, 20, 19, 25, 27, 26, 12, 11, 10, 17, 16, 18, 15, 14, 13, 8, 7, 9, 4, 6, 5, 1, 3, 2 ], 
  [ 22, 24, 23, 20, 19, 21, 27, 26, 25, 11, 10, 12, 16, 18, 17, 14, 13, 15, 7, 9, 8, 6, 5, 4, 3, 2, 1 ], 
  [ 20, 19, 21, 25, 27, 26, 23, 22, 24, 17, 16, 18, 13, 15, 14, 10, 12, 11, 6, 5, 4, 1, 3, 2, 8, 7, 9 ], 
  [ 19, 21, 20, 27, 26, 25, 22, 24, 23, 16, 18, 17, 15, 14, 13, 12, 11, 10, 5, 4, 6, 3, 2, 1, 7, 9, 8 ], 
  [ 21, 20, 19, 26, 25, 27, 24, 23, 22, 18, 17, 16, 14, 13, 15, 11, 10, 12, 4, 6, 5, 2, 1, 3, 9, 8, 7 ], 
  [ 25, 27, 26, 24, 23, 22, 21, 20, 19, 14, 13, 15, 12, 11, 10, 16, 18, 17, 1, 3, 2, 9, 8, 7, 4, 6, 5 ], 
  [ 27, 26, 25, 23, 22, 24, 20, 19, 21, 13, 15, 14, 11, 10, 12, 18, 17, 16, 3, 2, 1, 8, 7, 9, 6, 5, 4 ], 
  [ 26, 25, 27, 22, 24, 23, 19, 21, 20, 15, 14, 13, 10, 12, 11, 17, 16, 18, 2, 1, 3, 7, 9, 8, 5, 4, 6 ], 
  [ 16, 18, 17, 15, 14, 13, 12, 11, 10, 4, 6, 5, 2, 1, 3, 9, 8, 7, 19, 21, 20, 27, 26, 25, 22, 24, 23 ], 
  [ 18, 17, 16, 14, 13, 15, 11, 10, 12, 6, 5, 4, 1, 3, 2, 8, 7, 9, 21, 20, 19, 26, 25, 27, 24, 23, 22 ], 
  [ 17, 16, 18, 13, 15, 14, 10, 12, 11, 5, 4, 6, 3, 2, 1, 7, 9, 8, 20, 19, 21, 25, 27, 26, 23, 22, 24 ], 
  [ 13, 15, 14, 11, 10, 12, 18, 17, 16, 3, 2, 1, 8, 7, 9, 6, 5, 4, 26, 25, 27, 22, 24, 23, 19, 21, 20 ], 
  [ 15, 14, 13, 10, 12, 11, 17, 16, 18, 2, 1, 3, 7, 9, 8, 5, 4, 6, 25, 27, 26, 24, 23, 22, 21, 20, 19 ], 
  [ 14, 13, 15, 12, 11, 10, 16, 18, 17, 1, 3, 2, 9, 8, 7, 4, 6, 5, 27, 26, 25, 23, 22, 24, 20, 19, 21 ], 
  [ 11, 10, 12, 16, 18, 17, 14, 13, 15, 8, 7, 9, 4, 6, 5, 1, 3, 2, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 10, 12, 11, 18, 17, 16, 13, 15, 14, 7, 9, 8, 6, 5, 4, 3, 2, 1, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 12, 11, 10, 17, 16, 18, 15, 14, 13, 9, 8, 7, 5, 4, 6, 2, 1, 3, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 38;
QUANDLES[27].rack[38] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 6, 5, 4, 24, 23, 22, 20, 19, 21, 25, 27, 26, 16, 18, 17, 13, 15, 14, 11, 10, 12 ], 
  [ 3, 2, 1, 9, 8, 7, 5, 4, 6, 23, 22, 24, 19, 21, 20, 27, 26, 25, 18, 17, 16, 15, 14, 13, 10, 12, 11 ], 
  [ 2, 1, 3, 8, 7, 9, 4, 6, 5, 22, 24, 23, 21, 20, 19, 26, 25, 27, 17, 16, 18, 14, 13, 15, 12, 11, 10 ], 
  [ 7, 9, 8, 4, 6, 5, 2, 1, 3, 19, 21, 20, 25, 27, 26, 24, 23, 22, 15, 14, 13, 11, 10, 12, 16, 18, 17 ], 
  [ 9, 8, 7, 6, 5, 4, 1, 3, 2, 21, 20, 19, 27, 26, 25, 23, 22, 24, 14, 13, 15, 10, 12, 11, 18, 17, 16 ], 
  [ 8, 7, 9, 5, 4, 6, 3, 2, 1, 20, 19, 21, 26, 25, 27, 22, 24, 23, 13, 15, 14, 12, 11, 10, 17, 16, 18 ], 
  [ 6, 5, 4, 2, 1, 3, 7, 9, 8, 26, 25, 27, 23, 22, 24, 21, 20, 19, 12, 11, 10, 18, 17, 16, 14, 13, 15 ], 
  [ 5, 4, 6, 1, 3, 2, 9, 8, 7, 25, 27, 26, 22, 24, 23, 20, 19, 21, 11, 10, 12, 17, 16, 18, 13, 15, 14 ], 
  [ 4, 6, 5, 3, 2, 1, 8, 7, 9, 27, 26, 25, 24, 23, 22, 19, 21, 20, 10, 12, 11, 16, 18, 17, 15, 14, 13 ], 
  [ 26, 25, 27, 23, 22, 24, 21, 20, 19, 10, 12, 11, 16, 18, 17, 15, 14, 13, 4, 6, 5, 3, 2, 1, 8, 7, 9 ], 
  [ 25, 27, 26, 22, 24, 23, 20, 19, 21, 12, 11, 10, 18, 17, 16, 14, 13, 15, 6, 5, 4, 2, 1, 3, 7, 9, 8 ], 
  [ 27, 26, 25, 24, 23, 22, 19, 21, 20, 11, 10, 12, 17, 16, 18, 13, 15, 14, 5, 4, 6, 1, 3, 2, 9, 8, 7 ], 
  [ 22, 24, 23, 21, 20, 19, 26, 25, 27, 16, 18, 17, 13, 15, 14, 11, 10, 12, 2, 1, 3, 8, 7, 9, 4, 6, 5 ], 
  [ 24, 23, 22, 20, 19, 21, 25, 27, 26, 18, 17, 16, 15, 14, 13, 10, 12, 11, 1, 3, 2, 7, 9, 8, 6, 5, 4 ], 
  [ 23, 22, 24, 19, 21, 20, 27, 26, 25, 17, 16, 18, 14, 13, 15, 12, 11, 10, 3, 2, 1, 9, 8, 7, 5, 4, 6 ], 
  [ 19, 21, 20, 25, 27, 26, 24, 23, 22, 15, 14, 13, 11, 10, 12, 16, 18, 17, 9, 8, 7, 6, 5, 4, 1, 3, 2 ], 
  [ 21, 20, 19, 27, 26, 25, 23, 22, 24, 14, 13, 15, 10, 12, 11, 18, 17, 16, 8, 7, 9, 5, 4, 6, 3, 2, 1 ], 
  [ 20, 19, 21, 26, 25, 27, 22, 24, 23, 13, 15, 14, 12, 11, 10, 17, 16, 18, 7, 9, 8, 4, 6, 5, 2, 1, 3 ], 
  [ 14, 13, 15, 10, 12, 11, 18, 17, 16, 9, 8, 7, 6, 5, 4, 1, 3, 2, 19, 21, 20, 25, 27, 26, 24, 23, 22 ], 
  [ 13, 15, 14, 12, 11, 10, 17, 16, 18, 8, 7, 9, 5, 4, 6, 3, 2, 1, 21, 20, 19, 27, 26, 25, 23, 22, 24 ], 
  [ 15, 14, 13, 11, 10, 12, 16, 18, 17, 7, 9, 8, 4, 6, 5, 2, 1, 3, 20, 19, 21, 26, 25, 27, 22, 24, 23 ], 
  [ 12, 11, 10, 18, 17, 16, 14, 13, 15, 5, 4, 6, 1, 3, 2, 9, 8, 7, 25, 27, 26, 22, 24, 23, 20, 19, 21 ], 
  [ 11, 10, 12, 17, 16, 18, 13, 15, 14, 4, 6, 5, 3, 2, 1, 8, 7, 9, 27, 26, 25, 24, 23, 22, 19, 21, 20 ], 
  [ 10, 12, 11, 16, 18, 17, 15, 14, 13, 6, 5, 4, 2, 1, 3, 7, 9, 8, 26, 25, 27, 23, 22, 24, 21, 20, 19 ], 
  [ 16, 18, 17, 13, 15, 14, 11, 10, 12, 2, 1, 3, 8, 7, 9, 4, 6, 5, 24, 23, 22, 20, 19, 21, 25, 27, 26 ], 
  [ 18, 17, 16, 15, 14, 13, 10, 12, 11, 1, 3, 2, 7, 9, 8, 6, 5, 4, 23, 22, 24, 19, 21, 20, 27, 26, 25 ], 
  [ 17, 16, 18, 14, 13, 15, 12, 11, 10, 3, 2, 1, 9, 8, 7, 5, 4, 6, 22, 24, 23, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 39;
QUANDLES[27].rack[39] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 4, 6, 5, 25, 27, 26, 24, 23, 22, 21, 20, 19, 15, 14, 13, 10, 12, 11, 17, 16, 18 ], 
  [ 3, 2, 1, 8, 7, 9, 6, 5, 4, 27, 26, 25, 23, 22, 24, 20, 19, 21, 14, 13, 15, 12, 11, 10, 16, 18, 17 ], 
  [ 2, 1, 3, 7, 9, 8, 5, 4, 6, 26, 25, 27, 22, 24, 23, 19, 21, 20, 13, 15, 14, 11, 10, 12, 18, 17, 16 ], 
  [ 8, 7, 9, 4, 6, 5, 1, 3, 2, 22, 24, 23, 20, 19, 21, 27, 26, 25, 11, 10, 12, 16, 18, 17, 14, 13, 15 ], 
  [ 7, 9, 8, 6, 5, 4, 3, 2, 1, 24, 23, 22, 19, 21, 20, 26, 25, 27, 10, 12, 11, 18, 17, 16, 13, 15, 14 ], 
  [ 9, 8, 7, 5, 4, 6, 2, 1, 3, 23, 22, 24, 21, 20, 19, 25, 27, 26, 12, 11, 10, 17, 16, 18, 15, 14, 13 ], 
  [ 5, 4, 6, 3, 2, 1, 7, 9, 8, 20, 19, 21, 25, 27, 26, 23, 22, 24, 16, 18, 17, 15, 14, 13, 12, 11, 10 ], 
  [ 4, 6, 5, 2, 1, 3, 9, 8, 7, 19, 21, 20, 27, 26, 25, 22, 24, 23, 18, 17, 16, 14, 13, 15, 11, 10, 12 ], 
  [ 6, 5, 4, 1, 3, 2, 8, 7, 9, 21, 20, 19, 26, 25, 27, 24, 23, 22, 17, 16, 18, 13, 15, 14, 10, 12, 11 ], 
  [ 24, 23, 22, 19, 21, 20, 26, 25, 27, 10, 12, 11, 18, 17, 16, 13, 15, 14, 7, 9, 8, 6, 5, 4, 3, 2, 1 ], 
  [ 23, 22, 24, 21, 20, 19, 25, 27, 26, 12, 11, 10, 17, 16, 18, 15, 14, 13, 9, 8, 7, 5, 4, 6, 2, 1, 3 ], 
  [ 22, 24, 23, 20, 19, 21, 27, 26, 25, 11, 10, 12, 16, 18, 17, 14, 13, 15, 8, 7, 9, 4, 6, 5, 1, 3, 2 ], 
  [ 20, 19, 21, 25, 27, 26, 23, 22, 24, 17, 16, 18, 13, 15, 14, 10, 12, 11, 4, 6, 5, 2, 1, 3, 9, 8, 7 ], 
  [ 19, 21, 20, 27, 26, 25, 22, 24, 23, 16, 18, 17, 15, 14, 13, 12, 11, 10, 6, 5, 4, 1, 3, 2, 8, 7, 9 ], 
  [ 21, 20, 19, 26, 25, 27, 24, 23, 22, 18, 17, 16, 14, 13, 15, 11, 10, 12, 5, 4, 6, 3, 2, 1, 7, 9, 8 ], 
  [ 25, 27, 26, 24, 23, 22, 21, 20, 19, 14, 13, 15, 12, 11, 10, 16, 18, 17, 2, 1, 3, 7, 9, 8, 5, 4, 6 ], 
  [ 27, 26, 25, 23, 22, 24, 20, 19, 21, 13, 15, 14, 11, 10, 12, 18, 17, 16, 1, 3, 2, 9, 8, 7, 4, 6, 5 ], 
  [ 26, 25, 27, 22, 24, 23, 19, 21, 20, 15, 14, 13, 10, 12, 11, 17, 16, 18, 3, 2, 1, 8, 7, 9, 6, 5, 4 ], 
  [ 16, 18, 17, 15, 14, 13, 12, 11, 10, 6, 5, 4, 1, 3, 2, 8, 7, 9, 19, 21, 20, 27, 26, 25, 22, 24, 23 ], 
  [ 18, 17, 16, 14, 13, 15, 11, 10, 12, 5, 4, 6, 3, 2, 1, 7, 9, 8, 21, 20, 19, 26, 25, 27, 24, 23, 22 ], 
  [ 17, 16, 18, 13, 15, 14, 10, 12, 11, 4, 6, 5, 2, 1, 3, 9, 8, 7, 20, 19, 21, 25, 27, 26, 23, 22, 24 ], 
  [ 13, 15, 14, 11, 10, 12, 18, 17, 16, 2, 1, 3, 7, 9, 8, 5, 4, 6, 26, 25, 27, 22, 24, 23, 19, 21, 20 ], 
  [ 15, 14, 13, 10, 12, 11, 17, 16, 18, 1, 3, 2, 9, 8, 7, 4, 6, 5, 25, 27, 26, 24, 23, 22, 21, 20, 19 ], 
  [ 14, 13, 15, 12, 11, 10, 16, 18, 17, 3, 2, 1, 8, 7, 9, 6, 5, 4, 27, 26, 25, 23, 22, 24, 20, 19, 21 ], 
  [ 11, 10, 12, 16, 18, 17, 14, 13, 15, 7, 9, 8, 6, 5, 4, 3, 2, 1, 23, 22, 24, 21, 20, 19, 25, 27, 26 ], 
  [ 10, 12, 11, 18, 17, 16, 13, 15, 14, 9, 8, 7, 5, 4, 6, 2, 1, 3, 22, 24, 23, 20, 19, 21, 27, 26, 25 ], 
  [ 12, 11, 10, 17, 16, 18, 15, 14, 13, 8, 7, 9, 4, 6, 5, 1, 3, 2, 24, 23, 22, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 40;
QUANDLES[27].rack[40] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 6, 5, 4, 23, 22, 24, 19, 21, 20, 27, 26, 25, 17, 16, 18, 14, 13, 15, 12, 11, 10 ], 
  [ 3, 2, 1, 9, 8, 7, 5, 4, 6, 22, 24, 23, 21, 20, 19, 26, 25, 27, 16, 18, 17, 13, 15, 14, 11, 10, 12 ], 
  [ 2, 1, 3, 8, 7, 9, 4, 6, 5, 24, 23, 22, 20, 19, 21, 25, 27, 26, 18, 17, 16, 15, 14, 13, 10, 12, 11 ], 
  [ 7, 9, 8, 4, 6, 5, 2, 1, 3, 21, 20, 19, 27, 26, 25, 23, 22, 24, 13, 15, 14, 12, 11, 10, 17, 16, 18 ], 
  [ 9, 8, 7, 6, 5, 4, 1, 3, 2, 20, 19, 21, 26, 25, 27, 22, 24, 23, 15, 14, 13, 11, 10, 12, 16, 18, 17 ], 
  [ 8, 7, 9, 5, 4, 6, 3, 2, 1, 19, 21, 20, 25, 27, 26, 24, 23, 22, 14, 13, 15, 10, 12, 11, 18, 17, 16 ], 
  [ 6, 5, 4, 2, 1, 3, 7, 9, 8, 25, 27, 26, 22, 24, 23, 20, 19, 21, 10, 12, 11, 16, 18, 17, 15, 14, 13 ], 
  [ 5, 4, 6, 1, 3, 2, 9, 8, 7, 27, 26, 25, 24, 23, 22, 19, 21, 20, 12, 11, 10, 18, 17, 16, 14, 13, 15 ], 
  [ 4, 6, 5, 3, 2, 1, 8, 7, 9, 26, 25, 27, 23, 22, 24, 21, 20, 19, 11, 10, 12, 17, 16, 18, 13, 15, 14 ], 
  [ 26, 25, 27, 23, 22, 24, 21, 20, 19, 10, 12, 11, 16, 18, 17, 15, 14, 13, 5, 4, 6, 1, 3, 2, 9, 8, 7 ], 
  [ 25, 27, 26, 22, 24, 23, 20, 19, 21, 12, 11, 10, 18, 17, 16, 14, 13, 15, 4, 6, 5, 3, 2, 1, 8, 7, 9 ], 
  [ 27, 26, 25, 24, 23, 22, 19, 21, 20, 11, 10, 12, 17, 16, 18, 13, 15, 14, 6, 5, 4, 2, 1, 3, 7, 9, 8 ], 
  [ 22, 24, 23, 21, 20, 19, 26, 25, 27, 16, 18, 17, 13, 15, 14, 11, 10, 12, 3, 2, 1, 9, 8, 7, 5, 4, 6 ], 
  [ 24, 23, 22, 20, 19, 21, 25, 27, 26, 18, 17, 16, 15, 14, 13, 10, 12, 11, 2, 1, 3, 8, 7, 9, 4, 6, 5 ], 
  [ 23, 22, 24, 19, 21, 20, 27, 26, 25, 17, 16, 18, 14, 13, 15, 12, 11, 10, 1, 3, 2, 7, 9, 8, 6, 5, 4 ], 
  [ 19, 21, 20, 25, 27, 26, 24, 23, 22, 15, 14, 13, 11, 10, 12, 16, 18, 17, 7, 9, 8, 4, 6, 5, 2, 1, 3 ], 
  [ 21, 20, 19, 27, 26, 25, 23, 22, 24, 14, 13, 15, 10, 12, 11, 18, 17, 16, 9, 8, 7, 6, 5, 4, 1, 3, 2 ], 
  [ 20, 19, 21, 26, 25, 27, 22, 24, 23, 13, 15, 14, 12, 11, 10, 17, 16, 18, 8, 7, 9, 5, 4, 6, 3, 2, 1 ], 
  [ 14, 13, 15, 10, 12, 11, 18, 17, 16, 8, 7, 9, 5, 4, 6, 3, 2, 1, 19, 21, 20, 25, 27, 26, 24, 23, 22 ], 
  [ 13, 15, 14, 12, 11, 10, 17, 16, 18, 7, 9, 8, 4, 6, 5, 2, 1, 3, 21, 20, 19, 27, 26, 25, 23, 22, 24 ], 
  [ 15, 14, 13, 11, 10, 12, 16, 18, 17, 9, 8, 7, 6, 5, 4, 1, 3, 2, 20, 19, 21, 26, 25, 27, 22, 24, 23 ], 
  [ 12, 11, 10, 18, 17, 16, 14, 13, 15, 4, 6, 5, 3, 2, 1, 8, 7, 9, 25, 27, 26, 22, 24, 23, 20, 19, 21 ], 
  [ 11, 10, 12, 17, 16, 18, 13, 15, 14, 6, 5, 4, 2, 1, 3, 7, 9, 8, 27, 26, 25, 24, 23, 22, 19, 21, 20 ], 
  [ 10, 12, 11, 16, 18, 17, 15, 14, 13, 5, 4, 6, 1, 3, 2, 9, 8, 7, 26, 25, 27, 23, 22, 24, 21, 20, 19 ], 
  [ 16, 18, 17, 13, 15, 14, 11, 10, 12, 1, 3, 2, 7, 9, 8, 6, 5, 4, 24, 23, 22, 20, 19, 21, 25, 27, 26 ], 
  [ 18, 17, 16, 15, 14, 13, 10, 12, 11, 3, 2, 1, 9, 8, 7, 5, 4, 6, 23, 22, 24, 19, 21, 20, 27, 26, 25 ], 
  [ 17, 16, 18, 14, 13, 15, 12, 11, 10, 2, 1, 3, 8, 7, 9, 4, 6, 5, 22, 24, 23, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 41;
QUANDLES[27].rack[41] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 4, 6, 5, 21, 20, 19, 25, 27, 26, 23, 22, 24, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 3, 2, 1, 9, 8, 7, 6, 5, 4, 20, 19, 21, 27, 26, 25, 22, 24, 23, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 2, 1, 3, 8, 7, 9, 5, 4, 6, 19, 21, 20, 26, 25, 27, 24, 23, 22, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 9, 8, 7, 4, 6, 5, 3, 2, 1, 25, 27, 26, 23, 22, 24, 19, 21, 20, 18, 17, 16, 13, 15, 14, 12, 11, 10 ], 
  [ 8, 7, 9, 6, 5, 4, 2, 1, 3, 27, 26, 25, 22, 24, 23, 21, 20, 19, 17, 16, 18, 15, 14, 13, 11, 10, 12 ], 
  [ 7, 9, 8, 5, 4, 6, 1, 3, 2, 26, 25, 27, 24, 23, 22, 20, 19, 21, 16, 18, 17, 14, 13, 15, 10, 12, 11 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 22, 24, 23, 21, 20, 19, 25, 27, 26, 14, 13, 15, 12, 11, 10, 18, 17, 16 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 24, 23, 22, 20, 19, 21, 27, 26, 25, 13, 15, 14, 11, 10, 12, 17, 16, 18 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 23, 22, 24, 19, 21, 20, 26, 25, 27, 15, 14, 13, 10, 12, 11, 16, 18, 17 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 8, 7, 9, 6, 5, 4 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 2, 1, 7, 9, 8, 5, 4, 6 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15, 2, 1, 3, 9, 8, 7, 4, 6, 5 ], 
  [ 25, 27, 26, 23, 22, 24, 19, 21, 20, 18, 17, 16, 13, 15, 14, 12, 11, 10, 8, 7, 9, 6, 5, 4, 2, 1, 3 ], 
  [ 27, 26, 25, 22, 24, 23, 21, 20, 19, 17, 16, 18, 15, 14, 13, 11, 10, 12, 7, 9, 8, 5, 4, 6, 1, 3, 2 ], 
  [ 26, 25, 27, 24, 23, 22, 20, 19, 21, 16, 18, 17, 14, 13, 15, 10, 12, 11, 9, 8, 7, 4, 6, 5, 3, 2, 1 ], 
  [ 24, 23, 22, 19, 21, 20, 25, 27, 26, 14, 13, 15, 11, 10, 12, 16, 18, 17, 5, 4, 6, 1, 3, 2, 8, 7, 9 ], 
  [ 23, 22, 24, 21, 20, 19, 27, 26, 25, 13, 15, 14, 10, 12, 11, 18, 17, 16, 4, 6, 5, 3, 2, 1, 7, 9, 8 ], 
  [ 22, 24, 23, 20, 19, 21, 26, 25, 27, 15, 14, 13, 12, 11, 10, 17, 16, 18, 6, 5, 4, 2, 1, 3, 9, 8, 7 ], 
  [ 11, 10, 12, 18, 17, 16, 13, 15, 14, 1, 3, 2, 9, 8, 7, 5, 4, 6, 19, 21, 20, 25, 27, 26, 22, 24, 23 ], 
  [ 10, 12, 11, 17, 16, 18, 15, 14, 13, 3, 2, 1, 8, 7, 9, 4, 6, 5, 21, 20, 19, 27, 26, 25, 24, 23, 22 ], 
  [ 12, 11, 10, 16, 18, 17, 14, 13, 15, 2, 1, 3, 7, 9, 8, 6, 5, 4, 20, 19, 21, 26, 25, 27, 23, 22, 24 ], 
  [ 18, 17, 16, 13, 15, 14, 12, 11, 10, 8, 7, 9, 6, 5, 4, 2, 1, 3, 27, 26, 25, 22, 24, 23, 21, 20, 19 ], 
  [ 17, 16, 18, 15, 14, 13, 11, 10, 12, 7, 9, 8, 5, 4, 6, 1, 3, 2, 26, 25, 27, 24, 23, 22, 20, 19, 21 ], 
  [ 16, 18, 17, 14, 13, 15, 10, 12, 11, 9, 8, 7, 4, 6, 5, 3, 2, 1, 25, 27, 26, 23, 22, 24, 19, 21, 20 ], 
  [ 15, 14, 13, 11, 10, 12, 18, 17, 16, 4, 6, 5, 2, 1, 3, 8, 7, 9, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 14, 13, 15, 10, 12, 11, 17, 16, 18, 6, 5, 4, 1, 3, 2, 7, 9, 8, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 13, 15, 14, 12, 11, 10, 16, 18, 17, 5, 4, 6, 3, 2, 1, 9, 8, 7, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 42;
QUANDLES[27].rack[42] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 19, 21, 20, 27, 26, 25, 23, 22, 24, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 21, 20, 19, 26, 25, 27, 22, 24, 23, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 20, 19, 21, 25, 27, 26, 24, 23, 22, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 8, 7, 9, 4, 6, 5, 1, 3, 2, 25, 27, 26, 24, 23, 22, 21, 20, 19, 16, 18, 17, 15, 14, 13, 12, 11, 10 ], 
  [ 7, 9, 8, 6, 5, 4, 3, 2, 1, 27, 26, 25, 23, 22, 24, 20, 19, 21, 18, 17, 16, 14, 13, 15, 11, 10, 12 ], 
  [ 9, 8, 7, 5, 4, 6, 2, 1, 3, 26, 25, 27, 22, 24, 23, 19, 21, 20, 17, 16, 18, 13, 15, 14, 10, 12, 11 ], 
  [ 6, 5, 4, 1, 3, 2, 7, 9, 8, 24, 23, 22, 21, 20, 19, 26, 25, 27, 14, 13, 15, 10, 12, 11, 17, 16, 18 ], 
  [ 5, 4, 6, 3, 2, 1, 9, 8, 7, 23, 22, 24, 20, 19, 21, 25, 27, 26, 13, 15, 14, 12, 11, 10, 16, 18, 17 ], 
  [ 4, 6, 5, 2, 1, 3, 8, 7, 9, 22, 24, 23, 19, 21, 20, 27, 26, 25, 15, 14, 13, 11, 10, 12, 18, 17, 16 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 10, 12, 11, 17, 16, 18, 15, 14, 13, 2, 1, 3, 7, 9, 8, 6, 5, 4 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 12, 11, 10, 16, 18, 17, 14, 13, 15, 1, 3, 2, 9, 8, 7, 5, 4, 6 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 11, 10, 12, 18, 17, 16, 13, 15, 14, 3, 2, 1, 8, 7, 9, 4, 6, 5 ], 
  [ 26, 25, 27, 22, 24, 23, 19, 21, 20, 17, 16, 18, 13, 15, 14, 10, 12, 11, 8, 7, 9, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 27, 26, 24, 23, 22, 21, 20, 19, 16, 18, 17, 15, 14, 13, 12, 11, 10, 7, 9, 8, 6, 5, 4, 3, 2, 1 ], 
  [ 27, 26, 25, 23, 22, 24, 20, 19, 21, 18, 17, 16, 14, 13, 15, 11, 10, 12, 9, 8, 7, 5, 4, 6, 2, 1, 3 ], 
  [ 24, 23, 22, 20, 19, 21, 27, 26, 25, 15, 14, 13, 10, 12, 11, 16, 18, 17, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 23, 22, 24, 19, 21, 20, 26, 25, 27, 14, 13, 15, 12, 11, 10, 18, 17, 16, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 22, 24, 23, 21, 20, 19, 25, 27, 26, 13, 15, 14, 11, 10, 12, 17, 16, 18, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 12, 11, 10, 17, 16, 18, 13, 15, 14, 3, 2, 1, 9, 8, 7, 6, 5, 4, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 11, 10, 12, 16, 18, 17, 15, 14, 13, 2, 1, 3, 8, 7, 9, 5, 4, 6, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 10, 12, 11, 18, 17, 16, 14, 13, 15, 1, 3, 2, 7, 9, 8, 4, 6, 5, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 18, 17, 16, 14, 13, 15, 11, 10, 12, 9, 8, 7, 5, 4, 6, 2, 1, 3, 26, 25, 27, 22, 24, 23, 19, 21, 20 ], 
  [ 17, 16, 18, 13, 15, 14, 10, 12, 11, 8, 7, 9, 4, 6, 5, 1, 3, 2, 25, 27, 26, 24, 23, 22, 21, 20, 19 ], 
  [ 16, 18, 17, 15, 14, 13, 12, 11, 10, 7, 9, 8, 6, 5, 4, 3, 2, 1, 27, 26, 25, 23, 22, 24, 20, 19, 21 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 4, 6, 5, 3, 2, 1, 7, 9, 8, 24, 23, 22, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 6, 5, 4, 2, 1, 3, 9, 8, 7, 23, 22, 24, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 5, 4, 6, 1, 3, 2, 8, 7, 9, 22, 24, 23, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 43;
QUANDLES[27].rack[43] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 4, 6, 5, 19, 21, 20, 26, 25, 27, 22, 24, 23, 10, 12, 11, 17, 16, 18, 13, 15, 14 ], 
  [ 3, 2, 1, 7, 9, 8, 6, 5, 4, 21, 20, 19, 25, 27, 26, 24, 23, 22, 12, 11, 10, 16, 18, 17, 15, 14, 13 ], 
  [ 2, 1, 3, 9, 8, 7, 5, 4, 6, 20, 19, 21, 27, 26, 25, 23, 22, 24, 11, 10, 12, 18, 17, 16, 14, 13, 15 ], 
  [ 8, 7, 9, 4, 6, 5, 3, 2, 1, 26, 25, 27, 24, 23, 22, 19, 21, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 7, 9, 8, 6, 5, 4, 2, 1, 3, 25, 27, 26, 23, 22, 24, 21, 20, 19, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 9, 8, 7, 5, 4, 6, 1, 3, 2, 27, 26, 25, 22, 24, 23, 20, 19, 21, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 4, 6, 5, 3, 2, 1, 7, 9, 8, 24, 23, 22, 21, 20, 19, 26, 25, 27, 13, 15, 14, 11, 10, 12, 17, 16, 18 ], 
  [ 6, 5, 4, 2, 1, 3, 9, 8, 7, 23, 22, 24, 20, 19, 21, 25, 27, 26, 15, 14, 13, 10, 12, 11, 16, 18, 17 ], 
  [ 5, 4, 6, 1, 3, 2, 8, 7, 9, 22, 24, 23, 19, 21, 20, 27, 26, 25, 14, 13, 15, 12, 11, 10, 18, 17, 16 ], 
  [ 19, 21, 20, 26, 25, 27, 22, 24, 23, 10, 12, 11, 17, 16, 18, 13, 15, 14, 1, 3, 2, 8, 7, 9, 4, 6, 5 ], 
  [ 21, 20, 19, 25, 27, 26, 24, 23, 22, 12, 11, 10, 16, 18, 17, 15, 14, 13, 3, 2, 1, 7, 9, 8, 6, 5, 4 ], 
  [ 20, 19, 21, 27, 26, 25, 23, 22, 24, 11, 10, 12, 18, 17, 16, 14, 13, 15, 2, 1, 3, 9, 8, 7, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 17, 16, 18, 13, 15, 14, 12, 11, 10, 8, 7, 9, 6, 5, 4, 1, 3, 2 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 16, 18, 17, 15, 14, 13, 11, 10, 12, 7, 9, 8, 5, 4, 6, 3, 2, 1 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 18, 17, 16, 14, 13, 15, 10, 12, 11, 9, 8, 7, 4, 6, 5, 2, 1, 3 ], 
  [ 22, 24, 23, 20, 19, 21, 26, 25, 27, 13, 15, 14, 12, 11, 10, 16, 18, 17, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 24, 23, 22, 19, 21, 20, 25, 27, 26, 15, 14, 13, 11, 10, 12, 18, 17, 16, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 23, 22, 24, 21, 20, 19, 27, 26, 25, 14, 13, 15, 10, 12, 11, 17, 16, 18, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 10, 12, 11, 17, 16, 18, 13, 15, 14, 1, 3, 2, 8, 7, 9, 4, 6, 5, 19, 21, 20, 26, 25, 27, 22, 24, 23 ], 
  [ 12, 11, 10, 16, 18, 17, 15, 14, 13, 3, 2, 1, 7, 9, 8, 6, 5, 4, 21, 20, 19, 25, 27, 26, 24, 23, 22 ], 
  [ 11, 10, 12, 18, 17, 16, 14, 13, 15, 2, 1, 3, 9, 8, 7, 5, 4, 6, 20, 19, 21, 27, 26, 25, 23, 22, 24 ], 
  [ 17, 16, 18, 15, 14, 13, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 27, 22, 24, 23, 21, 20, 19 ], 
  [ 16, 18, 17, 14, 13, 15, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3, 25, 27, 26, 24, 23, 22, 20, 19, 21 ], 
  [ 18, 17, 16, 13, 15, 14, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2, 27, 26, 25, 23, 22, 24, 19, 21, 20 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 4, 6, 5, 2, 1, 3, 8, 7, 9, 22, 24, 23, 21, 20, 19, 25, 27, 26 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 6, 5, 4, 1, 3, 2, 7, 9, 8, 24, 23, 22, 20, 19, 21, 27, 26, 25 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 5, 4, 6, 3, 2, 1, 9, 8, 7, 23, 22, 24, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 44;
QUANDLES[27].rack[44] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 4, 6, 5, 21, 20, 19, 25, 27, 26, 24, 23, 22, 11, 10, 12, 18, 17, 16, 14, 13, 15 ], 
  [ 3, 2, 1, 7, 9, 8, 6, 5, 4, 20, 19, 21, 27, 26, 25, 23, 22, 24, 10, 12, 11, 17, 16, 18, 13, 15, 14 ], 
  [ 2, 1, 3, 9, 8, 7, 5, 4, 6, 19, 21, 20, 26, 25, 27, 22, 24, 23, 12, 11, 10, 16, 18, 17, 15, 14, 13 ], 
  [ 8, 7, 9, 4, 6, 5, 3, 2, 1, 25, 27, 26, 23, 22, 24, 21, 20, 19, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 7, 9, 8, 6, 5, 4, 2, 1, 3, 27, 26, 25, 22, 24, 23, 20, 19, 21, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 9, 8, 7, 5, 4, 6, 1, 3, 2, 26, 25, 27, 24, 23, 22, 19, 21, 20, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 4, 6, 5, 3, 2, 1, 7, 9, 8, 23, 22, 24, 20, 19, 21, 25, 27, 26, 14, 13, 15, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 2, 1, 3, 9, 8, 7, 22, 24, 23, 19, 21, 20, 27, 26, 25, 13, 15, 14, 11, 10, 12, 17, 16, 18 ], 
  [ 5, 4, 6, 1, 3, 2, 8, 7, 9, 24, 23, 22, 21, 20, 19, 26, 25, 27, 15, 14, 13, 10, 12, 11, 16, 18, 17 ], 
  [ 20, 19, 21, 27, 26, 25, 23, 22, 24, 10, 12, 11, 17, 16, 18, 13, 15, 14, 3, 2, 1, 7, 9, 8, 6, 5, 4 ], 
  [ 19, 21, 20, 26, 25, 27, 22, 24, 23, 12, 11, 10, 16, 18, 17, 15, 14, 13, 2, 1, 3, 9, 8, 7, 5, 4, 6 ], 
  [ 21, 20, 19, 25, 27, 26, 24, 23, 22, 11, 10, 12, 18, 17, 16, 14, 13, 15, 1, 3, 2, 8, 7, 9, 4, 6, 5 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 13, 15, 14, 12, 11, 10, 7, 9, 8, 5, 4, 6, 3, 2, 1 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 15, 14, 13, 11, 10, 12, 9, 8, 7, 4, 6, 5, 2, 1, 3 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 14, 13, 15, 10, 12, 11, 8, 7, 9, 6, 5, 4, 1, 3, 2 ], 
  [ 23, 22, 24, 21, 20, 19, 27, 26, 25, 13, 15, 14, 12, 11, 10, 16, 18, 17, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 22, 24, 23, 20, 19, 21, 26, 25, 27, 15, 14, 13, 11, 10, 12, 18, 17, 16, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 24, 23, 22, 19, 21, 20, 25, 27, 26, 14, 13, 15, 10, 12, 11, 17, 16, 18, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 12, 11, 10, 16, 18, 17, 15, 14, 13, 2, 1, 3, 9, 8, 7, 5, 4, 6, 19, 21, 20, 26, 25, 27, 22, 24, 23 ], 
  [ 11, 10, 12, 18, 17, 16, 14, 13, 15, 1, 3, 2, 8, 7, 9, 4, 6, 5, 21, 20, 19, 25, 27, 26, 24, 23, 22 ], 
  [ 10, 12, 11, 17, 16, 18, 13, 15, 14, 3, 2, 1, 7, 9, 8, 6, 5, 4, 20, 19, 21, 27, 26, 25, 23, 22, 24 ], 
  [ 16, 18, 17, 14, 13, 15, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2, 26, 25, 27, 22, 24, 23, 21, 20, 19 ], 
  [ 18, 17, 16, 13, 15, 14, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 27, 26, 24, 23, 22, 20, 19, 21 ], 
  [ 17, 16, 18, 15, 14, 13, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3, 27, 26, 25, 23, 22, 24, 19, 21, 20 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 5, 4, 6, 3, 2, 1, 9, 8, 7, 22, 24, 23, 21, 20, 19, 25, 27, 26 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 4, 6, 5, 2, 1, 3, 8, 7, 9, 24, 23, 22, 20, 19, 21, 27, 26, 25 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 6, 5, 4, 1, 3, 2, 7, 9, 8, 23, 22, 24, 19, 21, 20, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 45;
QUANDLES[27].rack[45] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 5, 4, 6, 20, 19, 21, 26, 25, 27, 24, 23, 22, 12, 11, 10, 18, 17, 16, 13, 15, 14 ], 
  [ 3, 2, 1, 9, 8, 7, 4, 6, 5, 19, 21, 20, 25, 27, 26, 23, 22, 24, 11, 10, 12, 17, 16, 18, 15, 14, 13 ], 
  [ 2, 1, 3, 8, 7, 9, 6, 5, 4, 21, 20, 19, 27, 26, 25, 22, 24, 23, 10, 12, 11, 16, 18, 17, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 2, 1, 3, 25, 27, 26, 22, 24, 23, 19, 21, 20, 18, 17, 16, 14, 13, 15, 10, 12, 11 ], 
  [ 8, 7, 9, 6, 5, 4, 1, 3, 2, 27, 26, 25, 24, 23, 22, 21, 20, 19, 17, 16, 18, 13, 15, 14, 12, 11, 10 ], 
  [ 7, 9, 8, 5, 4, 6, 3, 2, 1, 26, 25, 27, 23, 22, 24, 20, 19, 21, 16, 18, 17, 15, 14, 13, 11, 10, 12 ], 
  [ 6, 5, 4, 1, 3, 2, 7, 9, 8, 24, 23, 22, 20, 19, 21, 27, 26, 25, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 5, 4, 6, 3, 2, 1, 9, 8, 7, 23, 22, 24, 19, 21, 20, 26, 25, 27, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 4, 6, 5, 2, 1, 3, 8, 7, 9, 22, 24, 23, 21, 20, 19, 25, 27, 26, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 21, 20, 19, 27, 26, 25, 22, 24, 23, 10, 12, 11, 16, 18, 17, 14, 13, 15, 2, 1, 3, 8, 7, 9, 6, 5, 4 ], 
  [ 20, 19, 21, 26, 25, 27, 24, 23, 22, 12, 11, 10, 18, 17, 16, 13, 15, 14, 1, 3, 2, 7, 9, 8, 5, 4, 6 ], 
  [ 19, 21, 20, 25, 27, 26, 23, 22, 24, 11, 10, 12, 17, 16, 18, 15, 14, 13, 3, 2, 1, 9, 8, 7, 4, 6, 5 ], 
  [ 27, 26, 25, 23, 22, 24, 19, 21, 20, 18, 17, 16, 13, 15, 14, 11, 10, 12, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 26, 25, 27, 22, 24, 23, 21, 20, 19, 17, 16, 18, 15, 14, 13, 10, 12, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 25, 27, 26, 24, 23, 22, 20, 19, 21, 16, 18, 17, 14, 13, 15, 12, 11, 10, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 15, 14, 13, 10, 12, 11, 16, 18, 17, 6, 5, 4, 2, 1, 3, 9, 8, 7 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 14, 13, 15, 12, 11, 10, 18, 17, 16, 5, 4, 6, 1, 3, 2, 8, 7, 9 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 13, 15, 14, 11, 10, 12, 17, 16, 18, 4, 6, 5, 3, 2, 1, 7, 9, 8 ], 
  [ 11, 10, 12, 17, 16, 18, 15, 14, 13, 3, 2, 1, 9, 8, 7, 4, 6, 5, 19, 21, 20, 25, 27, 26, 23, 22, 24 ], 
  [ 10, 12, 11, 16, 18, 17, 14, 13, 15, 2, 1, 3, 8, 7, 9, 6, 5, 4, 21, 20, 19, 27, 26, 25, 22, 24, 23 ], 
  [ 12, 11, 10, 18, 17, 16, 13, 15, 14, 1, 3, 2, 7, 9, 8, 5, 4, 6, 20, 19, 21, 26, 25, 27, 24, 23, 22 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 9, 8, 7, 5, 4, 6, 1, 3, 2, 27, 26, 25, 22, 24, 23, 20, 19, 21 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 8, 7, 9, 4, 6, 5, 3, 2, 1, 26, 25, 27, 24, 23, 22, 19, 21, 20 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 7, 9, 8, 6, 5, 4, 2, 1, 3, 25, 27, 26, 23, 22, 24, 21, 20, 19 ], 
  [ 15, 14, 13, 11, 10, 12, 18, 17, 16, 5, 4, 6, 2, 1, 3, 7, 9, 8, 24, 23, 22, 19, 21, 20, 25, 27, 26 ], 
  [ 14, 13, 15, 10, 12, 11, 17, 16, 18, 4, 6, 5, 1, 3, 2, 9, 8, 7, 23, 22, 24, 21, 20, 19, 27, 26, 25 ], 
  [ 13, 15, 14, 12, 11, 10, 16, 18, 17, 6, 5, 4, 3, 2, 1, 8, 7, 9, 22, 24, 23, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 46;
QUANDLES[27].rack[46] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 7, 9, 8, 5, 4, 6, 19, 21, 20, 25, 27, 26, 23, 22, 24, 10, 12, 11, 16, 18, 17, 14, 13, 15 ], 
  [ 3, 2, 1, 9, 8, 7, 4, 6, 5, 21, 20, 19, 27, 26, 25, 22, 24, 23, 12, 11, 10, 18, 17, 16, 13, 15, 14 ], 
  [ 2, 1, 3, 8, 7, 9, 6, 5, 4, 20, 19, 21, 26, 25, 27, 24, 23, 22, 11, 10, 12, 17, 16, 18, 15, 14, 13 ], 
  [ 9, 8, 7, 4, 6, 5, 2, 1, 3, 27, 26, 25, 24, 23, 22, 21, 20, 19, 16, 18, 17, 15, 14, 13, 11, 10, 12 ], 
  [ 8, 7, 9, 6, 5, 4, 1, 3, 2, 26, 25, 27, 23, 22, 24, 20, 19, 21, 18, 17, 16, 14, 13, 15, 10, 12, 11 ], 
  [ 7, 9, 8, 5, 4, 6, 3, 2, 1, 25, 27, 26, 22, 24, 23, 19, 21, 20, 17, 16, 18, 13, 15, 14, 12, 11, 10 ], 
  [ 6, 5, 4, 1, 3, 2, 7, 9, 8, 23, 22, 24, 19, 21, 20, 26, 25, 27, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 5, 4, 6, 3, 2, 1, 9, 8, 7, 22, 24, 23, 21, 20, 19, 25, 27, 26, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 4, 6, 5, 2, 1, 3, 8, 7, 9, 24, 23, 22, 20, 19, 21, 27, 26, 25, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 19, 21, 20, 25, 27, 26, 23, 22, 24, 10, 12, 11, 16, 18, 17, 14, 13, 15, 1, 3, 2, 7, 9, 8, 5, 4, 6 ], 
  [ 21, 20, 19, 27, 26, 25, 22, 24, 23, 12, 11, 10, 18, 17, 16, 13, 15, 14, 3, 2, 1, 9, 8, 7, 4, 6, 5 ], 
  [ 20, 19, 21, 26, 25, 27, 24, 23, 22, 11, 10, 12, 17, 16, 18, 15, 14, 13, 2, 1, 3, 8, 7, 9, 6, 5, 4 ], 
  [ 25, 27, 26, 24, 23, 22, 20, 19, 21, 18, 17, 16, 13, 15, 14, 11, 10, 12, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 27, 26, 25, 23, 22, 24, 19, 21, 20, 17, 16, 18, 15, 14, 13, 10, 12, 11, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 26, 25, 27, 22, 24, 23, 21, 20, 19, 16, 18, 17, 14, 13, 15, 12, 11, 10, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 15, 14, 13, 10, 12, 11, 16, 18, 17, 5, 4, 6, 1, 3, 2, 8, 7, 9 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 14, 13, 15, 12, 11, 10, 18, 17, 16, 4, 6, 5, 3, 2, 1, 7, 9, 8 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 13, 15, 14, 11, 10, 12, 17, 16, 18, 6, 5, 4, 2, 1, 3, 9, 8, 7 ], 
  [ 10, 12, 11, 16, 18, 17, 14, 13, 15, 1, 3, 2, 7, 9, 8, 5, 4, 6, 19, 21, 20, 25, 27, 26, 23, 22, 24 ], 
  [ 12, 11, 10, 18, 17, 16, 13, 15, 14, 3, 2, 1, 9, 8, 7, 4, 6, 5, 21, 20, 19, 27, 26, 25, 22, 24, 23 ], 
  [ 11, 10, 12, 17, 16, 18, 15, 14, 13, 2, 1, 3, 8, 7, 9, 6, 5, 4, 20, 19, 21, 26, 25, 27, 24, 23, 22 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 7, 9, 8, 6, 5, 4, 2, 1, 3, 27, 26, 25, 22, 24, 23, 20, 19, 21 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 9, 8, 7, 5, 4, 6, 1, 3, 2, 26, 25, 27, 24, 23, 22, 19, 21, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 8, 7, 9, 4, 6, 5, 3, 2, 1, 25, 27, 26, 23, 22, 24, 21, 20, 19 ], 
  [ 14, 13, 15, 10, 12, 11, 17, 16, 18, 6, 5, 4, 3, 2, 1, 8, 7, 9, 24, 23, 22, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 12, 11, 10, 16, 18, 17, 5, 4, 6, 2, 1, 3, 7, 9, 8, 23, 22, 24, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 11, 10, 12, 18, 17, 16, 4, 6, 5, 1, 3, 2, 9, 8, 7, 22, 24, 23, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 47;
QUANDLES[27].rack[47] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 21, 20, 19, 25, 27, 26, 23, 22, 24, 17, 16, 18, 14, 13, 15, 10, 12, 11 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 20, 19, 21, 27, 26, 25, 22, 24, 23, 16, 18, 17, 13, 15, 14, 12, 11, 10 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 19, 21, 20, 26, 25, 27, 24, 23, 22, 18, 17, 16, 15, 14, 13, 11, 10, 12 ], 
  [ 7, 9, 8, 4, 6, 5, 3, 2, 1, 27, 26, 25, 24, 23, 22, 20, 19, 21, 13, 15, 14, 11, 10, 12, 16, 18, 17 ], 
  [ 9, 8, 7, 6, 5, 4, 2, 1, 3, 26, 25, 27, 23, 22, 24, 19, 21, 20, 15, 14, 13, 10, 12, 11, 18, 17, 16 ], 
  [ 8, 7, 9, 5, 4, 6, 1, 3, 2, 25, 27, 26, 22, 24, 23, 21, 20, 19, 14, 13, 15, 12, 11, 10, 17, 16, 18 ], 
  [ 4, 6, 5, 2, 1, 3, 7, 9, 8, 24, 23, 22, 19, 21, 20, 27, 26, 25, 11, 10, 12, 18, 17, 16, 13, 15, 14 ], 
  [ 6, 5, 4, 1, 3, 2, 9, 8, 7, 23, 22, 24, 21, 20, 19, 26, 25, 27, 10, 12, 11, 17, 16, 18, 15, 14, 13 ], 
  [ 5, 4, 6, 3, 2, 1, 8, 7, 9, 22, 24, 23, 20, 19, 21, 25, 27, 26, 12, 11, 10, 16, 18, 17, 14, 13, 15 ], 
  [ 23, 22, 24, 21, 20, 19, 26, 25, 27, 10, 12, 11, 17, 16, 18, 15, 14, 13, 9, 8, 7, 6, 5, 4, 2, 1, 3 ], 
  [ 22, 24, 23, 20, 19, 21, 25, 27, 26, 12, 11, 10, 16, 18, 17, 14, 13, 15, 8, 7, 9, 5, 4, 6, 1, 3, 2 ], 
  [ 24, 23, 22, 19, 21, 20, 27, 26, 25, 11, 10, 12, 18, 17, 16, 13, 15, 14, 7, 9, 8, 4, 6, 5, 3, 2, 1 ], 
  [ 20, 19, 21, 27, 26, 25, 22, 24, 23, 16, 18, 17, 13, 15, 14, 12, 11, 10, 5, 4, 6, 3, 2, 1, 8, 7, 9 ], 
  [ 19, 21, 20, 26, 25, 27, 24, 23, 22, 18, 17, 16, 15, 14, 13, 11, 10, 12, 4, 6, 5, 2, 1, 3, 7, 9, 8 ], 
  [ 21, 20, 19, 25, 27, 26, 23, 22, 24, 17, 16, 18, 14, 13, 15, 10, 12, 11, 6, 5, 4, 1, 3, 2, 9, 8, 7 ], 
  [ 27, 26, 25, 24, 23, 22, 20, 19, 21, 13, 15, 14, 11, 10, 12, 16, 18, 17, 3, 2, 1, 7, 9, 8, 5, 4, 6 ], 
  [ 26, 25, 27, 23, 22, 24, 19, 21, 20, 15, 14, 13, 10, 12, 11, 18, 17, 16, 2, 1, 3, 9, 8, 7, 4, 6, 5 ], 
  [ 25, 27, 26, 22, 24, 23, 21, 20, 19, 14, 13, 15, 12, 11, 10, 17, 16, 18, 1, 3, 2, 8, 7, 9, 6, 5, 4 ], 
  [ 15, 14, 13, 10, 12, 11, 18, 17, 16, 2, 1, 3, 9, 8, 7, 4, 6, 5, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 14, 13, 15, 12, 11, 10, 17, 16, 18, 1, 3, 2, 8, 7, 9, 6, 5, 4, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 13, 15, 14, 11, 10, 12, 16, 18, 17, 3, 2, 1, 7, 9, 8, 5, 4, 6, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 12, 11, 10, 16, 18, 17, 14, 13, 15, 8, 7, 9, 5, 4, 6, 1, 3, 2, 25, 27, 26, 22, 24, 23, 21, 20, 19 ], 
  [ 11, 10, 12, 18, 17, 16, 13, 15, 14, 7, 9, 8, 4, 6, 5, 3, 2, 1, 27, 26, 25, 24, 23, 22, 20, 19, 21 ], 
  [ 10, 12, 11, 17, 16, 18, 15, 14, 13, 9, 8, 7, 6, 5, 4, 2, 1, 3, 26, 25, 27, 23, 22, 24, 19, 21, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 12, 11, 10, 5, 4, 6, 3, 2, 1, 8, 7, 9, 22, 24, 23, 20, 19, 21, 25, 27, 26 ], 
  [ 18, 17, 16, 15, 14, 13, 11, 10, 12, 4, 6, 5, 2, 1, 3, 7, 9, 8, 24, 23, 22, 19, 21, 20, 27, 26, 25 ], 
  [ 17, 16, 18, 14, 13, 15, 10, 12, 11, 6, 5, 4, 1, 3, 2, 9, 8, 7, 23, 22, 24, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 48;
QUANDLES[27].rack[48] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 5, 4, 6, 26, 25, 27, 24, 23, 22, 21, 20, 19, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 3, 2, 1, 8, 7, 9, 4, 6, 5, 25, 27, 26, 23, 22, 24, 20, 19, 21, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 2, 1, 3, 7, 9, 8, 6, 5, 4, 27, 26, 25, 22, 24, 23, 19, 21, 20, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 9, 8, 7, 4, 6, 5, 1, 3, 2, 24, 23, 22, 20, 19, 21, 26, 25, 27, 16, 18, 17, 14, 13, 15, 11, 10, 12 ], 
  [ 8, 7, 9, 6, 5, 4, 3, 2, 1, 23, 22, 24, 19, 21, 20, 25, 27, 26, 18, 17, 16, 13, 15, 14, 10, 12, 11 ], 
  [ 7, 9, 8, 5, 4, 6, 2, 1, 3, 22, 24, 23, 21, 20, 19, 27, 26, 25, 17, 16, 18, 15, 14, 13, 12, 11, 10 ], 
  [ 5, 4, 6, 1, 3, 2, 7, 9, 8, 21, 20, 19, 26, 25, 27, 22, 24, 23, 15, 14, 13, 11, 10, 12, 17, 16, 18 ], 
  [ 4, 6, 5, 3, 2, 1, 9, 8, 7, 20, 19, 21, 25, 27, 26, 24, 23, 22, 14, 13, 15, 10, 12, 11, 16, 18, 17 ], 
  [ 6, 5, 4, 2, 1, 3, 8, 7, 9, 19, 21, 20, 27, 26, 25, 23, 22, 24, 13, 15, 14, 12, 11, 10, 18, 17, 16 ], 
  [ 25, 27, 26, 23, 22, 24, 20, 19, 21, 10, 12, 11, 18, 17, 16, 14, 13, 15, 4, 6, 5, 3, 2, 1, 9, 8, 7 ], 
  [ 27, 26, 25, 22, 24, 23, 19, 21, 20, 12, 11, 10, 17, 16, 18, 13, 15, 14, 6, 5, 4, 2, 1, 3, 8, 7, 9 ], 
  [ 26, 25, 27, 24, 23, 22, 21, 20, 19, 11, 10, 12, 16, 18, 17, 15, 14, 13, 5, 4, 6, 1, 3, 2, 7, 9, 8 ], 
  [ 23, 22, 24, 19, 21, 20, 25, 27, 26, 18, 17, 16, 13, 15, 14, 10, 12, 11, 3, 2, 1, 8, 7, 9, 4, 6, 5 ], 
  [ 22, 24, 23, 21, 20, 19, 27, 26, 25, 17, 16, 18, 15, 14, 13, 12, 11, 10, 2, 1, 3, 7, 9, 8, 6, 5, 4 ], 
  [ 24, 23, 22, 20, 19, 21, 26, 25, 27, 16, 18, 17, 14, 13, 15, 11, 10, 12, 1, 3, 2, 9, 8, 7, 5, 4, 6 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 14, 13, 15, 10, 12, 11, 16, 18, 17, 9, 8, 7, 4, 6, 5, 1, 3, 2 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 13, 15, 14, 12, 11, 10, 18, 17, 16, 8, 7, 9, 6, 5, 4, 3, 2, 1 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 15, 14, 13, 11, 10, 12, 17, 16, 18, 7, 9, 8, 5, 4, 6, 2, 1, 3 ], 
  [ 12, 11, 10, 17, 16, 18, 13, 15, 14, 6, 5, 4, 2, 1, 3, 8, 7, 9, 19, 21, 20, 27, 26, 25, 23, 22, 24 ], 
  [ 11, 10, 12, 16, 18, 17, 15, 14, 13, 5, 4, 6, 1, 3, 2, 7, 9, 8, 21, 20, 19, 26, 25, 27, 22, 24, 23 ], 
  [ 10, 12, 11, 18, 17, 16, 14, 13, 15, 4, 6, 5, 3, 2, 1, 9, 8, 7, 20, 19, 21, 25, 27, 26, 24, 23, 22 ], 
  [ 17, 16, 18, 15, 14, 13, 12, 11, 10, 2, 1, 3, 7, 9, 8, 6, 5, 4, 27, 26, 25, 22, 24, 23, 19, 21, 20 ], 
  [ 16, 18, 17, 14, 13, 15, 11, 10, 12, 1, 3, 2, 9, 8, 7, 5, 4, 6, 26, 25, 27, 24, 23, 22, 21, 20, 19 ], 
  [ 18, 17, 16, 13, 15, 14, 10, 12, 11, 3, 2, 1, 8, 7, 9, 4, 6, 5, 25, 27, 26, 23, 22, 24, 20, 19, 21 ], 
  [ 13, 15, 14, 12, 11, 10, 18, 17, 16, 8, 7, 9, 6, 5, 4, 3, 2, 1, 23, 22, 24, 19, 21, 20, 25, 27, 26 ], 
  [ 15, 14, 13, 11, 10, 12, 17, 16, 18, 7, 9, 8, 5, 4, 6, 2, 1, 3, 22, 24, 23, 21, 20, 19, 27, 26, 25 ], 
  [ 14, 13, 15, 10, 12, 11, 16, 18, 17, 9, 8, 7, 4, 6, 5, 1, 3, 2, 24, 23, 22, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 49;
QUANDLES[27].rack[49] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 20, 19, 21, 27, 26, 25, 22, 24, 23, 18, 17, 16, 15, 14, 13, 11, 10, 12 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 19, 21, 20, 26, 25, 27, 24, 23, 22, 17, 16, 18, 14, 13, 15, 10, 12, 11 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 21, 20, 19, 25, 27, 26, 23, 22, 24, 16, 18, 17, 13, 15, 14, 12, 11, 10 ], 
  [ 7, 9, 8, 4, 6, 5, 3, 2, 1, 26, 25, 27, 23, 22, 24, 19, 21, 20, 14, 13, 15, 12, 11, 10, 17, 16, 18 ], 
  [ 9, 8, 7, 6, 5, 4, 2, 1, 3, 25, 27, 26, 22, 24, 23, 21, 20, 19, 13, 15, 14, 11, 10, 12, 16, 18, 17 ], 
  [ 8, 7, 9, 5, 4, 6, 1, 3, 2, 27, 26, 25, 24, 23, 22, 20, 19, 21, 15, 14, 13, 10, 12, 11, 18, 17, 16 ], 
  [ 4, 6, 5, 2, 1, 3, 7, 9, 8, 23, 22, 24, 21, 20, 19, 26, 25, 27, 12, 11, 10, 16, 18, 17, 14, 13, 15 ], 
  [ 6, 5, 4, 1, 3, 2, 9, 8, 7, 22, 24, 23, 20, 19, 21, 25, 27, 26, 11, 10, 12, 18, 17, 16, 13, 15, 14 ], 
  [ 5, 4, 6, 3, 2, 1, 8, 7, 9, 24, 23, 22, 19, 21, 20, 27, 26, 25, 10, 12, 11, 17, 16, 18, 15, 14, 13 ], 
  [ 24, 23, 22, 19, 21, 20, 27, 26, 25, 10, 12, 11, 17, 16, 18, 15, 14, 13, 8, 7, 9, 5, 4, 6, 1, 3, 2 ], 
  [ 23, 22, 24, 21, 20, 19, 26, 25, 27, 12, 11, 10, 16, 18, 17, 14, 13, 15, 7, 9, 8, 4, 6, 5, 3, 2, 1 ], 
  [ 22, 24, 23, 20, 19, 21, 25, 27, 26, 11, 10, 12, 18, 17, 16, 13, 15, 14, 9, 8, 7, 6, 5, 4, 2, 1, 3 ], 
  [ 21, 20, 19, 25, 27, 26, 23, 22, 24, 16, 18, 17, 13, 15, 14, 12, 11, 10, 4, 6, 5, 2, 1, 3, 7, 9, 8 ], 
  [ 20, 19, 21, 27, 26, 25, 22, 24, 23, 18, 17, 16, 15, 14, 13, 11, 10, 12, 6, 5, 4, 1, 3, 2, 9, 8, 7 ], 
  [ 19, 21, 20, 26, 25, 27, 24, 23, 22, 17, 16, 18, 14, 13, 15, 10, 12, 11, 5, 4, 6, 3, 2, 1, 8, 7, 9 ], 
  [ 25, 27, 26, 22, 24, 23, 21, 20, 19, 13, 15, 14, 11, 10, 12, 16, 18, 17, 2, 1, 3, 9, 8, 7, 4, 6, 5 ], 
  [ 27, 26, 25, 24, 23, 22, 20, 19, 21, 15, 14, 13, 10, 12, 11, 18, 17, 16, 1, 3, 2, 8, 7, 9, 6, 5, 4 ], 
  [ 26, 25, 27, 23, 22, 24, 19, 21, 20, 14, 13, 15, 12, 11, 10, 17, 16, 18, 3, 2, 1, 7, 9, 8, 5, 4, 6 ], 
  [ 14, 13, 15, 12, 11, 10, 17, 16, 18, 3, 2, 1, 7, 9, 8, 5, 4, 6, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 13, 15, 14, 11, 10, 12, 16, 18, 17, 2, 1, 3, 9, 8, 7, 4, 6, 5, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 15, 14, 13, 10, 12, 11, 18, 17, 16, 1, 3, 2, 8, 7, 9, 6, 5, 4, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 11, 10, 12, 18, 17, 16, 13, 15, 14, 9, 8, 7, 6, 5, 4, 2, 1, 3, 25, 27, 26, 22, 24, 23, 21, 20, 19 ], 
  [ 10, 12, 11, 17, 16, 18, 15, 14, 13, 8, 7, 9, 5, 4, 6, 1, 3, 2, 27, 26, 25, 24, 23, 22, 20, 19, 21 ], 
  [ 12, 11, 10, 16, 18, 17, 14, 13, 15, 7, 9, 8, 4, 6, 5, 3, 2, 1, 26, 25, 27, 23, 22, 24, 19, 21, 20 ], 
  [ 18, 17, 16, 15, 14, 13, 11, 10, 12, 6, 5, 4, 1, 3, 2, 9, 8, 7, 22, 24, 23, 20, 19, 21, 25, 27, 26 ], 
  [ 17, 16, 18, 14, 13, 15, 10, 12, 11, 5, 4, 6, 3, 2, 1, 8, 7, 9, 24, 23, 22, 19, 21, 20, 27, 26, 25 ], 
  [ 16, 18, 17, 13, 15, 14, 12, 11, 10, 4, 6, 5, 2, 1, 3, 7, 9, 8, 23, 22, 24, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 50;
QUANDLES[27].rack[50] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 5, 4, 6, 25, 27, 26, 23, 22, 24, 20, 19, 21, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 3, 2, 1, 8, 7, 9, 4, 6, 5, 27, 26, 25, 22, 24, 23, 19, 21, 20, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 2, 1, 3, 7, 9, 8, 6, 5, 4, 26, 25, 27, 24, 23, 22, 21, 20, 19, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 9, 8, 7, 4, 6, 5, 1, 3, 2, 23, 22, 24, 19, 21, 20, 25, 27, 26, 17, 16, 18, 15, 14, 13, 12, 11, 10 ], 
  [ 8, 7, 9, 6, 5, 4, 3, 2, 1, 22, 24, 23, 21, 20, 19, 27, 26, 25, 16, 18, 17, 14, 13, 15, 11, 10, 12 ], 
  [ 7, 9, 8, 5, 4, 6, 2, 1, 3, 24, 23, 22, 20, 19, 21, 26, 25, 27, 18, 17, 16, 13, 15, 14, 10, 12, 11 ], 
  [ 5, 4, 6, 1, 3, 2, 7, 9, 8, 20, 19, 21, 25, 27, 26, 24, 23, 22, 13, 15, 14, 12, 11, 10, 18, 17, 16 ], 
  [ 4, 6, 5, 3, 2, 1, 9, 8, 7, 19, 21, 20, 27, 26, 25, 23, 22, 24, 15, 14, 13, 11, 10, 12, 17, 16, 18 ], 
  [ 6, 5, 4, 2, 1, 3, 8, 7, 9, 21, 20, 19, 26, 25, 27, 22, 24, 23, 14, 13, 15, 10, 12, 11, 16, 18, 17 ], 
  [ 26, 25, 27, 24, 23, 22, 21, 20, 19, 10, 12, 11, 18, 17, 16, 14, 13, 15, 6, 5, 4, 2, 1, 3, 8, 7, 9 ], 
  [ 25, 27, 26, 23, 22, 24, 20, 19, 21, 12, 11, 10, 17, 16, 18, 13, 15, 14, 5, 4, 6, 1, 3, 2, 7, 9, 8 ], 
  [ 27, 26, 25, 22, 24, 23, 19, 21, 20, 11, 10, 12, 16, 18, 17, 15, 14, 13, 4, 6, 5, 3, 2, 1, 9, 8, 7 ], 
  [ 24, 23, 22, 20, 19, 21, 26, 25, 27, 18, 17, 16, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 6, 5, 4 ], 
  [ 23, 22, 24, 19, 21, 20, 25, 27, 26, 17, 16, 18, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 5, 4, 6 ], 
  [ 22, 24, 23, 21, 20, 19, 27, 26, 25, 16, 18, 17, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 4, 6, 5 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 14, 13, 15, 10, 12, 11, 16, 18, 17, 8, 7, 9, 6, 5, 4, 3, 2, 1 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 13, 15, 14, 12, 11, 10, 18, 17, 16, 7, 9, 8, 5, 4, 6, 2, 1, 3 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 15, 14, 13, 11, 10, 12, 17, 16, 18, 9, 8, 7, 4, 6, 5, 1, 3, 2 ], 
  [ 11, 10, 12, 16, 18, 17, 15, 14, 13, 4, 6, 5, 3, 2, 1, 9, 8, 7, 19, 21, 20, 27, 26, 25, 23, 22, 24 ], 
  [ 10, 12, 11, 18, 17, 16, 14, 13, 15, 6, 5, 4, 2, 1, 3, 8, 7, 9, 21, 20, 19, 26, 25, 27, 22, 24, 23 ], 
  [ 12, 11, 10, 17, 16, 18, 13, 15, 14, 5, 4, 6, 1, 3, 2, 7, 9, 8, 20, 19, 21, 25, 27, 26, 24, 23, 22 ], 
  [ 16, 18, 17, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 4, 6, 5, 27, 26, 25, 22, 24, 23, 19, 21, 20 ], 
  [ 18, 17, 16, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 6, 5, 4, 26, 25, 27, 24, 23, 22, 21, 20, 19 ], 
  [ 17, 16, 18, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 5, 4, 6, 25, 27, 26, 23, 22, 24, 20, 19, 21 ], 
  [ 15, 14, 13, 11, 10, 12, 17, 16, 18, 9, 8, 7, 4, 6, 5, 1, 3, 2, 23, 22, 24, 19, 21, 20, 25, 27, 26 ], 
  [ 14, 13, 15, 10, 12, 11, 16, 18, 17, 8, 7, 9, 6, 5, 4, 3, 2, 1, 22, 24, 23, 21, 20, 19, 27, 26, 25 ], 
  [ 13, 15, 14, 12, 11, 10, 18, 17, 16, 7, 9, 8, 5, 4, 6, 2, 1, 3, 24, 23, 22, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 51;
QUANDLES[27].rack[51] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 19, 21, 20, 26, 25, 27, 24, 23, 22, 16, 18, 17, 13, 15, 14, 12, 11, 10 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 21, 20, 19, 25, 27, 26, 23, 22, 24, 18, 17, 16, 15, 14, 13, 11, 10, 12 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 20, 19, 21, 27, 26, 25, 22, 24, 23, 17, 16, 18, 14, 13, 15, 10, 12, 11 ], 
  [ 7, 9, 8, 4, 6, 5, 3, 2, 1, 25, 27, 26, 22, 24, 23, 21, 20, 19, 15, 14, 13, 10, 12, 11, 18, 17, 16 ], 
  [ 9, 8, 7, 6, 5, 4, 2, 1, 3, 27, 26, 25, 24, 23, 22, 20, 19, 21, 14, 13, 15, 12, 11, 10, 17, 16, 18 ], 
  [ 8, 7, 9, 5, 4, 6, 1, 3, 2, 26, 25, 27, 23, 22, 24, 19, 21, 20, 13, 15, 14, 11, 10, 12, 16, 18, 17 ], 
  [ 4, 6, 5, 2, 1, 3, 7, 9, 8, 22, 24, 23, 20, 19, 21, 25, 27, 26, 10, 12, 11, 17, 16, 18, 15, 14, 13 ], 
  [ 6, 5, 4, 1, 3, 2, 9, 8, 7, 24, 23, 22, 19, 21, 20, 27, 26, 25, 12, 11, 10, 16, 18, 17, 14, 13, 15 ], 
  [ 5, 4, 6, 3, 2, 1, 8, 7, 9, 23, 22, 24, 21, 20, 19, 26, 25, 27, 11, 10, 12, 18, 17, 16, 13, 15, 14 ], 
  [ 22, 24, 23, 20, 19, 21, 25, 27, 26, 10, 12, 11, 17, 16, 18, 15, 14, 13, 7, 9, 8, 4, 6, 5, 3, 2, 1 ], 
  [ 24, 23, 22, 19, 21, 20, 27, 26, 25, 12, 11, 10, 16, 18, 17, 14, 13, 15, 9, 8, 7, 6, 5, 4, 2, 1, 3 ], 
  [ 23, 22, 24, 21, 20, 19, 26, 25, 27, 11, 10, 12, 18, 17, 16, 13, 15, 14, 8, 7, 9, 5, 4, 6, 1, 3, 2 ], 
  [ 19, 21, 20, 26, 25, 27, 24, 23, 22, 16, 18, 17, 13, 15, 14, 12, 11, 10, 6, 5, 4, 1, 3, 2, 9, 8, 7 ], 
  [ 21, 20, 19, 25, 27, 26, 23, 22, 24, 18, 17, 16, 15, 14, 13, 11, 10, 12, 5, 4, 6, 3, 2, 1, 8, 7, 9 ], 
  [ 20, 19, 21, 27, 26, 25, 22, 24, 23, 17, 16, 18, 14, 13, 15, 10, 12, 11, 4, 6, 5, 2, 1, 3, 7, 9, 8 ], 
  [ 26, 25, 27, 23, 22, 24, 19, 21, 20, 13, 15, 14, 11, 10, 12, 16, 18, 17, 1, 3, 2, 8, 7, 9, 6, 5, 4 ], 
  [ 25, 27, 26, 22, 24, 23, 21, 20, 19, 15, 14, 13, 10, 12, 11, 18, 17, 16, 3, 2, 1, 7, 9, 8, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 20, 19, 21, 14, 13, 15, 12, 11, 10, 17, 16, 18, 2, 1, 3, 9, 8, 7, 4, 6, 5 ], 
  [ 13, 15, 14, 11, 10, 12, 16, 18, 17, 1, 3, 2, 8, 7, 9, 6, 5, 4, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 15, 14, 13, 10, 12, 11, 18, 17, 16, 3, 2, 1, 7, 9, 8, 5, 4, 6, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 14, 13, 15, 12, 11, 10, 17, 16, 18, 2, 1, 3, 9, 8, 7, 4, 6, 5, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 10, 12, 11, 17, 16, 18, 15, 14, 13, 7, 9, 8, 4, 6, 5, 3, 2, 1, 25, 27, 26, 22, 24, 23, 21, 20, 19 ], 
  [ 12, 11, 10, 16, 18, 17, 14, 13, 15, 9, 8, 7, 6, 5, 4, 2, 1, 3, 27, 26, 25, 24, 23, 22, 20, 19, 21 ], 
  [ 11, 10, 12, 18, 17, 16, 13, 15, 14, 8, 7, 9, 5, 4, 6, 1, 3, 2, 26, 25, 27, 23, 22, 24, 19, 21, 20 ], 
  [ 17, 16, 18, 14, 13, 15, 10, 12, 11, 4, 6, 5, 2, 1, 3, 7, 9, 8, 22, 24, 23, 20, 19, 21, 25, 27, 26 ], 
  [ 16, 18, 17, 13, 15, 14, 12, 11, 10, 6, 5, 4, 1, 3, 2, 9, 8, 7, 24, 23, 22, 19, 21, 20, 27, 26, 25 ], 
  [ 18, 17, 16, 15, 14, 13, 11, 10, 12, 5, 4, 6, 3, 2, 1, 8, 7, 9, 23, 22, 24, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 52;
QUANDLES[27].rack[52] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 5, 4, 6, 27, 26, 25, 22, 24, 23, 19, 21, 20, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 3, 2, 1, 8, 7, 9, 4, 6, 5, 26, 25, 27, 24, 23, 22, 21, 20, 19, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 2, 1, 3, 7, 9, 8, 6, 5, 4, 25, 27, 26, 23, 22, 24, 20, 19, 21, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 9, 8, 7, 4, 6, 5, 1, 3, 2, 22, 24, 23, 21, 20, 19, 27, 26, 25, 18, 17, 16, 13, 15, 14, 10, 12, 11 ], 
  [ 8, 7, 9, 6, 5, 4, 3, 2, 1, 24, 23, 22, 20, 19, 21, 26, 25, 27, 17, 16, 18, 15, 14, 13, 12, 11, 10 ], 
  [ 7, 9, 8, 5, 4, 6, 2, 1, 3, 23, 22, 24, 19, 21, 20, 25, 27, 26, 16, 18, 17, 14, 13, 15, 11, 10, 12 ], 
  [ 5, 4, 6, 1, 3, 2, 7, 9, 8, 19, 21, 20, 27, 26, 25, 23, 22, 24, 14, 13, 15, 10, 12, 11, 16, 18, 17 ], 
  [ 4, 6, 5, 3, 2, 1, 9, 8, 7, 21, 20, 19, 26, 25, 27, 22, 24, 23, 13, 15, 14, 12, 11, 10, 18, 17, 16 ], 
  [ 6, 5, 4, 2, 1, 3, 8, 7, 9, 20, 19, 21, 25, 27, 26, 24, 23, 22, 15, 14, 13, 11, 10, 12, 17, 16, 18 ], 
  [ 27, 26, 25, 22, 24, 23, 19, 21, 20, 10, 12, 11, 18, 17, 16, 14, 13, 15, 5, 4, 6, 1, 3, 2, 7, 9, 8 ], 
  [ 26, 25, 27, 24, 23, 22, 21, 20, 19, 12, 11, 10, 17, 16, 18, 13, 15, 14, 4, 6, 5, 3, 2, 1, 9, 8, 7 ], 
  [ 25, 27, 26, 23, 22, 24, 20, 19, 21, 11, 10, 12, 16, 18, 17, 15, 14, 13, 6, 5, 4, 2, 1, 3, 8, 7, 9 ], 
  [ 22, 24, 23, 21, 20, 19, 27, 26, 25, 18, 17, 16, 13, 15, 14, 10, 12, 11, 1, 3, 2, 9, 8, 7, 5, 4, 6 ], 
  [ 24, 23, 22, 20, 19, 21, 26, 25, 27, 17, 16, 18, 15, 14, 13, 12, 11, 10, 3, 2, 1, 8, 7, 9, 4, 6, 5 ], 
  [ 23, 22, 24, 19, 21, 20, 25, 27, 26, 16, 18, 17, 14, 13, 15, 11, 10, 12, 2, 1, 3, 7, 9, 8, 6, 5, 4 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 14, 13, 15, 10, 12, 11, 16, 18, 17, 7, 9, 8, 5, 4, 6, 2, 1, 3 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 13, 15, 14, 12, 11, 10, 18, 17, 16, 9, 8, 7, 4, 6, 5, 1, 3, 2 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 15, 14, 13, 11, 10, 12, 17, 16, 18, 8, 7, 9, 6, 5, 4, 3, 2, 1 ], 
  [ 10, 12, 11, 18, 17, 16, 14, 13, 15, 5, 4, 6, 1, 3, 2, 7, 9, 8, 19, 21, 20, 27, 26, 25, 23, 22, 24 ], 
  [ 12, 11, 10, 17, 16, 18, 13, 15, 14, 4, 6, 5, 3, 2, 1, 9, 8, 7, 21, 20, 19, 26, 25, 27, 22, 24, 23 ], 
  [ 11, 10, 12, 16, 18, 17, 15, 14, 13, 6, 5, 4, 2, 1, 3, 8, 7, 9, 20, 19, 21, 25, 27, 26, 24, 23, 22 ], 
  [ 18, 17, 16, 13, 15, 14, 10, 12, 11, 1, 3, 2, 9, 8, 7, 5, 4, 6, 27, 26, 25, 22, 24, 23, 19, 21, 20 ], 
  [ 17, 16, 18, 15, 14, 13, 12, 11, 10, 3, 2, 1, 8, 7, 9, 4, 6, 5, 26, 25, 27, 24, 23, 22, 21, 20, 19 ], 
  [ 16, 18, 17, 14, 13, 15, 11, 10, 12, 2, 1, 3, 7, 9, 8, 6, 5, 4, 25, 27, 26, 23, 22, 24, 20, 19, 21 ], 
  [ 14, 13, 15, 10, 12, 11, 16, 18, 17, 7, 9, 8, 5, 4, 6, 2, 1, 3, 23, 22, 24, 19, 21, 20, 25, 27, 26 ], 
  [ 13, 15, 14, 12, 11, 10, 18, 17, 16, 9, 8, 7, 4, 6, 5, 1, 3, 2, 22, 24, 23, 21, 20, 19, 27, 26, 25 ], 
  [ 15, 14, 13, 11, 10, 12, 17, 16, 18, 8, 7, 9, 6, 5, 4, 3, 2, 1, 24, 23, 22, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 53;
QUANDLES[27].rack[53] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 24, 23, 22, 21, 20, 19, 26, 25, 27, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 23, 22, 24, 20, 19, 21, 25, 27, 26, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 22, 24, 23, 19, 21, 20, 27, 26, 25, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 21, 20, 19, 26, 25, 27, 23, 22, 24, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 21, 25, 27, 26, 22, 24, 23, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 19, 21, 20, 27, 26, 25, 24, 23, 22, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 26, 25, 27, 23, 22, 24, 20, 19, 21, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 25, 27, 26, 22, 24, 23, 19, 21, 20, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 27, 26, 25, 24, 23, 22, 21, 20, 19, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 10, 12, 11, 18, 17, 16, 15, 14, 13, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 12, 11, 10, 17, 16, 18, 14, 13, 15, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 11, 10, 12, 16, 18, 17, 13, 15, 14, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 16, 18, 17, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 18, 17, 16, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 17, 16, 18, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 14, 13, 15, 11, 10, 12, 16, 18, 17, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 13, 15, 14, 10, 12, 11, 18, 17, 16, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 15, 14, 13, 12, 11, 10, 17, 16, 18, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 7, 9, 8, 4, 6, 5, 1, 3, 2, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 8, 7, 9, 5, 4, 6, 2, 1, 3, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 4, 6, 5, 1, 3, 2, 9, 8, 7, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 6, 5, 4, 3, 2, 1, 8, 7, 9, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 5, 4, 6, 2, 1, 3, 7, 9, 8, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 6, 5, 4, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 5, 4, 6, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 4, 6, 5, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 54;
QUANDLES[27].rack[54] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 26, 25, 27, 23, 22, 24, 20, 19, 21, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 25, 27, 26, 22, 24, 23, 19, 21, 20, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 27, 26, 25, 24, 23, 22, 21, 20, 19, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 25, 27, 26, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 27, 26, 25, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 26, 25, 27, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 20, 19, 21, 25, 27, 26, 22, 24, 23, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 19, 21, 20, 27, 26, 25, 24, 23, 22, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 21, 20, 19, 26, 25, 27, 23, 22, 24, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 10, 12, 11, 18, 17, 16, 15, 14, 13, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 12, 11, 10, 17, 16, 18, 14, 13, 15, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 11, 10, 12, 16, 18, 17, 13, 15, 14, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 16, 18, 17, 13, 15, 14, 10, 12, 11, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 18, 17, 16, 15, 14, 13, 12, 11, 10, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 17, 16, 18, 14, 13, 15, 11, 10, 12, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 14, 13, 15, 11, 10, 12, 16, 18, 17, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 13, 15, 14, 10, 12, 11, 18, 17, 16, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 15, 14, 13, 12, 11, 10, 17, 16, 18, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 5, 4, 6, 2, 1, 3, 7, 9, 8, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 4, 6, 5, 1, 3, 2, 9, 8, 7, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 6, 5, 4, 3, 2, 1, 8, 7, 9, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 2, 1, 3, 7, 9, 8, 4, 6, 5, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 1, 3, 2, 9, 8, 7, 6, 5, 4, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 3, 2, 1, 8, 7, 9, 5, 4, 6, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 7, 9, 8, 4, 6, 5, 1, 3, 2, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 8, 7, 9, 5, 4, 6, 2, 1, 3, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 55;
QUANDLES[27].rack[55] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 6, 5, 4, 23, 22, 24, 20, 19, 21, 25, 27, 26, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 3, 2, 1, 8, 7, 9, 5, 4, 6, 22, 24, 23, 19, 21, 20, 27, 26, 25, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 2, 1, 3, 7, 9, 8, 4, 6, 5, 24, 23, 22, 21, 20, 19, 26, 25, 27, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 7, 9, 8, 4, 6, 5, 1, 3, 2, 20, 19, 21, 25, 27, 26, 22, 24, 23, 13, 15, 14, 10, 12, 11, 18, 17, 16 ], 
  [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 21, 20, 27, 26, 25, 24, 23, 22, 15, 14, 13, 12, 11, 10, 17, 16, 18 ], 
  [ 8, 7, 9, 5, 4, 6, 2, 1, 3, 21, 20, 19, 26, 25, 27, 23, 22, 24, 14, 13, 15, 11, 10, 12, 16, 18, 17 ], 
  [ 5, 4, 6, 2, 1, 3, 7, 9, 8, 25, 27, 26, 22, 24, 23, 19, 21, 20, 10, 12, 11, 18, 17, 16, 15, 14, 13 ], 
  [ 4, 6, 5, 1, 3, 2, 9, 8, 7, 27, 26, 25, 24, 23, 22, 21, 20, 19, 12, 11, 10, 17, 16, 18, 14, 13, 15 ], 
  [ 6, 5, 4, 3, 2, 1, 8, 7, 9, 26, 25, 27, 23, 22, 24, 20, 19, 21, 11, 10, 12, 16, 18, 17, 13, 15, 14 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 10, 12, 11, 18, 17, 16, 15, 14, 13, 5, 4, 6, 2, 1, 3, 7, 9, 8 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 12, 11, 10, 17, 16, 18, 14, 13, 15, 4, 6, 5, 1, 3, 2, 9, 8, 7 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 11, 10, 12, 16, 18, 17, 13, 15, 14, 6, 5, 4, 3, 2, 1, 8, 7, 9 ], 
  [ 22, 24, 23, 19, 21, 20, 27, 26, 25, 16, 18, 17, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 4, 6, 5 ], 
  [ 24, 23, 22, 21, 20, 19, 26, 25, 27, 18, 17, 16, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 6, 5, 4 ], 
  [ 23, 22, 24, 20, 19, 21, 25, 27, 26, 17, 16, 18, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 5, 4, 6 ], 
  [ 19, 21, 20, 27, 26, 25, 24, 23, 22, 14, 13, 15, 11, 10, 12, 16, 18, 17, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 21, 20, 19, 26, 25, 27, 23, 22, 24, 13, 15, 14, 10, 12, 11, 18, 17, 16, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 20, 19, 21, 25, 27, 26, 22, 24, 23, 15, 14, 13, 12, 11, 10, 17, 16, 18, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 14, 13, 15, 11, 10, 12, 16, 18, 17, 7, 9, 8, 4, 6, 5, 1, 3, 2, 19, 21, 20, 27, 26, 25, 24, 23, 22 ], 
  [ 13, 15, 14, 10, 12, 11, 18, 17, 16, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 26, 25, 27, 23, 22, 24 ], 
  [ 15, 14, 13, 12, 11, 10, 17, 16, 18, 8, 7, 9, 5, 4, 6, 2, 1, 3, 20, 19, 21, 25, 27, 26, 22, 24, 23 ], 
  [ 11, 10, 12, 16, 18, 17, 13, 15, 14, 4, 6, 5, 1, 3, 2, 9, 8, 7, 25, 27, 26, 22, 24, 23, 19, 21, 20 ], 
  [ 10, 12, 11, 18, 17, 16, 15, 14, 13, 6, 5, 4, 3, 2, 1, 8, 7, 9, 27, 26, 25, 24, 23, 22, 21, 20, 19 ], 
  [ 12, 11, 10, 17, 16, 18, 14, 13, 15, 5, 4, 6, 2, 1, 3, 7, 9, 8, 26, 25, 27, 23, 22, 24, 20, 19, 21 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 1, 3, 2, 9, 8, 7, 6, 5, 4, 23, 22, 24, 20, 19, 21, 25, 27, 26 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 3, 2, 1, 8, 7, 9, 5, 4, 6, 22, 24, 23, 19, 21, 20, 27, 26, 25 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 2, 1, 3, 7, 9, 8, 4, 6, 5, 24, 23, 22, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 56;
QUANDLES[27].rack[56] := rec( size := 27, matrix :=
[ [ 1, 8, 6, 2, 9, 4, 3, 7, 5, 23, 22, 24, 20, 19, 21, 26, 25, 27, 18, 12, 15, 11, 14, 17, 13, 16, 10 ], 
  [ 4, 2, 9, 5, 3, 7, 6, 1, 8, 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 11, 14, 10, 13, 16, 15, 18, 12 ], 
  [ 7, 5, 3, 8, 6, 1, 9, 4, 2, 20, 19, 21, 26, 25, 27, 23, 22, 24, 16, 10, 13, 12, 15, 18, 14, 17, 11 ], 
  [ 6, 1, 8, 4, 2, 9, 5, 3, 7, 25, 27, 26, 22, 24, 23, 19, 21, 20, 15, 18, 12, 17, 11, 14, 10, 13, 16 ], 
  [ 9, 4, 2, 7, 5, 3, 8, 6, 1, 19, 21, 20, 25, 27, 26, 22, 24, 23, 14, 17, 11, 16, 10, 13, 12, 15, 18 ], 
  [ 3, 7, 5, 1, 8, 6, 2, 9, 4, 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 16, 10, 18, 12, 15, 11, 14, 17 ], 
  [ 8, 6, 1, 9, 4, 2, 7, 5, 3, 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 15, 18, 14, 17, 11, 16, 10, 13 ], 
  [ 2, 9, 4, 3, 7, 5, 1, 8, 6, 24, 23, 22, 21, 20, 19, 27, 26, 25, 11, 14, 17, 13, 16, 10, 18, 12, 15 ], 
  [ 5, 3, 7, 6, 1, 8, 4, 2, 9, 27, 26, 25, 24, 23, 22, 21, 20, 19, 10, 13, 16, 15, 18, 12, 17, 11, 14 ], 
  [ 27, 21, 24, 20, 23, 26, 22, 25, 19, 10, 17, 15, 11, 18, 13, 12, 16, 14, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 26, 20, 23, 19, 22, 25, 24, 27, 21, 13, 11, 18, 14, 12, 16, 15, 10, 17, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 25, 19, 22, 21, 24, 27, 23, 26, 20, 16, 14, 12, 17, 15, 10, 18, 13, 11, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 24, 27, 21, 26, 20, 23, 19, 22, 25, 15, 10, 17, 13, 11, 18, 14, 12, 16, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 23, 26, 20, 25, 19, 22, 21, 24, 27, 18, 13, 11, 16, 14, 12, 17, 15, 10, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 22, 25, 19, 27, 21, 24, 20, 23, 26, 12, 16, 14, 10, 17, 15, 11, 18, 13, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 21, 24, 27, 23, 26, 20, 25, 19, 22, 17, 15, 10, 18, 13, 11, 16, 14, 12, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 20, 23, 26, 22, 25, 19, 27, 21, 24, 11, 18, 13, 12, 16, 14, 10, 17, 15, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 19, 22, 25, 24, 27, 21, 26, 20, 23, 14, 12, 16, 15, 10, 17, 13, 11, 18, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 9, 3, 6, 2, 5, 8, 4, 7, 1, 19, 26, 24, 20, 27, 22, 21, 25, 23 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 2, 5, 1, 4, 7, 6, 9, 3, 22, 20, 27, 23, 21, 25, 24, 19, 26 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 7, 1, 4, 3, 6, 9, 5, 8, 2, 25, 23, 21, 26, 24, 19, 27, 22, 20 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 6, 9, 3, 8, 2, 5, 1, 4, 7, 24, 19, 26, 22, 20, 27, 23, 21, 25 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 5, 8, 2, 7, 1, 4, 3, 6, 9, 27, 22, 20, 25, 23, 21, 26, 24, 19 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 4, 7, 1, 9, 3, 6, 2, 5, 8, 21, 25, 23, 19, 26, 24, 20, 27, 22 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 3, 6, 9, 5, 8, 2, 7, 1, 4, 26, 24, 19, 27, 22, 20, 25, 23, 21 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 2, 5, 8, 4, 7, 1, 9, 3, 6, 20, 27, 22, 21, 25, 23, 19, 26, 24 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 1, 4, 7, 6, 9, 3, 8, 2, 5, 23, 21, 25, 24, 19, 26, 22, 20, 27 ] ]);
QUANDLES[27].implemented := 57;
QUANDLES[27].rack[57] := rec( size := 27, matrix :=
[ [ 1, 4, 7, 6, 9, 3, 8, 2, 5, 27, 22, 20, 25, 23, 21, 26, 24, 19, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 8, 2, 5, 1, 4, 7, 6, 9, 3, 22, 20, 27, 23, 21, 25, 24, 19, 26, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 6, 9, 3, 8, 2, 5, 1, 4, 7, 20, 27, 22, 21, 25, 23, 19, 26, 24, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 2, 5, 8, 4, 7, 1, 9, 3, 6, 25, 23, 21, 26, 24, 19, 27, 22, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 9, 3, 6, 2, 5, 8, 4, 7, 1, 23, 21, 25, 24, 19, 26, 22, 20, 27, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 4, 7, 1, 9, 3, 6, 2, 5, 8, 21, 25, 23, 19, 26, 24, 20, 27, 22, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 3, 6, 9, 5, 8, 2, 7, 1, 4, 26, 24, 19, 27, 22, 20, 25, 23, 21, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 7, 1, 4, 3, 6, 9, 5, 8, 2, 24, 19, 26, 22, 20, 27, 23, 21, 25, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 5, 8, 2, 7, 1, 4, 3, 6, 9, 19, 26, 24, 20, 27, 22, 21, 25, 23, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 10, 13, 16, 15, 18, 12, 17, 11, 14, 9, 4, 2, 7, 5, 3, 8, 6, 1 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 11, 14, 10, 13, 16, 15, 18, 12, 4, 2, 9, 5, 3, 7, 6, 1, 8 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 15, 18, 12, 17, 11, 14, 10, 13, 16, 2, 9, 4, 3, 7, 5, 1, 8, 6 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 11, 14, 17, 13, 16, 10, 18, 12, 15, 7, 5, 3, 8, 6, 1, 9, 4, 2 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 18, 12, 15, 11, 14, 17, 13, 16, 10, 5, 3, 7, 6, 1, 8, 4, 2, 9 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 13, 16, 10, 18, 12, 15, 11, 14, 17, 3, 7, 5, 1, 8, 6, 2, 9, 4 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 12, 15, 18, 14, 17, 11, 16, 10, 13, 8, 6, 1, 9, 4, 2, 7, 5, 3 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 16, 10, 13, 12, 15, 18, 14, 17, 11, 6, 1, 8, 4, 2, 9, 5, 3, 7 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 14, 17, 11, 16, 10, 13, 12, 15, 18, 1, 8, 6, 2, 9, 4, 3, 7, 5 ], 
  [ 18, 13, 11, 16, 14, 12, 17, 15, 10, 5, 4, 6, 2, 1, 3, 8, 7, 9, 19, 22, 25, 24, 27, 21, 26, 20, 23 ], 
  [ 13, 11, 18, 14, 12, 16, 15, 10, 17, 8, 7, 9, 5, 4, 6, 2, 1, 3, 26, 20, 23, 19, 22, 25, 24, 27, 21 ], 
  [ 11, 18, 13, 12, 16, 14, 10, 17, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6, 24, 27, 21, 26, 20, 23, 19, 22, 25 ], 
  [ 16, 14, 12, 17, 15, 10, 18, 13, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2, 20, 23, 26, 22, 25, 19, 27, 21, 24 ], 
  [ 14, 12, 16, 15, 10, 17, 13, 11, 18, 1, 3, 2, 7, 9, 8, 4, 6, 5, 27, 21, 24, 20, 23, 26, 22, 25, 19 ], 
  [ 12, 16, 14, 10, 17, 15, 11, 18, 13, 4, 6, 5, 1, 3, 2, 7, 9, 8, 22, 25, 19, 27, 21, 24, 20, 23, 26 ], 
  [ 17, 15, 10, 18, 13, 11, 16, 14, 12, 3, 2, 1, 9, 8, 7, 6, 5, 4, 21, 24, 27, 23, 26, 20, 25, 19, 22 ], 
  [ 15, 10, 17, 13, 11, 18, 14, 12, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7, 25, 19, 22, 21, 24, 27, 23, 26, 20 ], 
  [ 10, 17, 15, 11, 18, 13, 12, 16, 14, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 26, 20, 25, 19, 22, 21, 24, 27 ] ]);
QUANDLES[27].implemented := 58;
QUANDLES[27].rack[58] := rec( size := 27, matrix :=
[ [ 1, 4, 7, 6, 9, 3, 8, 2, 5, 19, 26, 24, 20, 27, 22, 21, 25, 23, 10, 12, 11, 16, 18, 17, 13, 15, 14 ], 
  [ 8, 2, 5, 1, 4, 7, 6, 9, 3, 26, 24, 19, 27, 22, 20, 25, 23, 21, 13, 15, 14, 10, 12, 11, 16, 18, 17 ], 
  [ 6, 9, 3, 8, 2, 5, 1, 4, 7, 24, 19, 26, 22, 20, 27, 23, 21, 25, 16, 18, 17, 13, 15, 14, 10, 12, 11 ], 
  [ 2, 5, 8, 4, 7, 1, 9, 3, 6, 20, 27, 22, 21, 25, 23, 19, 26, 24, 15, 14, 13, 12, 11, 10, 18, 17, 16 ], 
  [ 9, 3, 6, 2, 5, 8, 4, 7, 1, 27, 22, 20, 25, 23, 21, 26, 24, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10 ], 
  [ 4, 7, 1, 9, 3, 6, 2, 5, 8, 22, 20, 27, 23, 21, 25, 24, 19, 26, 12, 11, 10, 18, 17, 16, 15, 14, 13 ], 
  [ 3, 6, 9, 5, 8, 2, 7, 1, 4, 21, 25, 23, 19, 26, 24, 20, 27, 22, 17, 16, 18, 14, 13, 15, 11, 10, 12 ], 
  [ 7, 1, 4, 3, 6, 9, 5, 8, 2, 25, 23, 21, 26, 24, 19, 27, 22, 20, 11, 10, 12, 17, 16, 18, 14, 13, 15 ], 
  [ 5, 8, 2, 7, 1, 4, 3, 6, 9, 23, 21, 25, 24, 19, 26, 22, 20, 27, 14, 13, 15, 11, 10, 12, 17, 16, 18 ], 
  [ 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 13, 16, 15, 18, 12, 17, 11, 14, 1, 8, 6, 2, 9, 4, 3, 7, 5 ], 
  [ 22, 24, 23, 19, 21, 20, 25, 27, 26, 17, 11, 14, 10, 13, 16, 15, 18, 12, 8, 6, 1, 9, 4, 2, 7, 5, 3 ], 
  [ 25, 27, 26, 22, 24, 23, 19, 21, 20, 15, 18, 12, 17, 11, 14, 10, 13, 16, 6, 1, 8, 4, 2, 9, 5, 3, 7 ], 
  [ 24, 23, 22, 21, 20, 19, 27, 26, 25, 11, 14, 17, 13, 16, 10, 18, 12, 15, 2, 9, 4, 3, 7, 5, 1, 8, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 12, 15, 11, 14, 17, 13, 16, 10, 9, 4, 2, 7, 5, 3, 8, 6, 1 ], 
  [ 21, 20, 19, 27, 26, 25, 24, 23, 22, 13, 16, 10, 18, 12, 15, 11, 14, 17, 4, 2, 9, 5, 3, 7, 6, 1, 8 ], 
  [ 26, 25, 27, 23, 22, 24, 20, 19, 21, 12, 15, 18, 14, 17, 11, 16, 10, 13, 3, 7, 5, 1, 8, 6, 2, 9, 4 ], 
  [ 20, 19, 21, 26, 25, 27, 23, 22, 24, 16, 10, 13, 12, 15, 18, 14, 17, 11, 7, 5, 3, 8, 6, 1, 9, 4, 2 ], 
  [ 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 17, 11, 16, 10, 13, 12, 15, 18, 5, 3, 7, 6, 1, 8, 4, 2, 9 ], 
  [ 10, 17, 15, 11, 18, 13, 12, 16, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5, 19, 22, 25, 24, 27, 21, 26, 20, 23 ], 
  [ 17, 15, 10, 18, 13, 11, 16, 14, 12, 4, 6, 5, 1, 3, 2, 7, 9, 8, 26, 20, 23, 19, 22, 25, 24, 27, 21 ], 
  [ 15, 10, 17, 13, 11, 18, 14, 12, 16, 7, 9, 8, 4, 6, 5, 1, 3, 2, 24, 27, 21, 26, 20, 23, 19, 22, 25 ], 
  [ 11, 18, 13, 12, 16, 14, 10, 17, 15, 6, 5, 4, 3, 2, 1, 9, 8, 7, 20, 23, 26, 22, 25, 19, 27, 21, 24 ], 
  [ 18, 13, 11, 16, 14, 12, 17, 15, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 21, 24, 20, 23, 26, 22, 25, 19 ], 
  [ 13, 11, 18, 14, 12, 16, 15, 10, 17, 3, 2, 1, 9, 8, 7, 6, 5, 4, 22, 25, 19, 27, 21, 24, 20, 23, 26 ], 
  [ 12, 16, 14, 10, 17, 15, 11, 18, 13, 8, 7, 9, 5, 4, 6, 2, 1, 3, 21, 24, 27, 23, 26, 20, 25, 19, 22 ], 
  [ 16, 14, 12, 17, 15, 10, 18, 13, 11, 2, 1, 3, 8, 7, 9, 5, 4, 6, 25, 19, 22, 21, 24, 27, 23, 26, 20 ], 
  [ 14, 12, 16, 15, 10, 17, 13, 11, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9, 23, 26, 20, 25, 19, 22, 21, 24, 27 ] ]);
QUANDLES[27].implemented := 59;
QUANDLES[27].rack[59] := rec( size := 27, matrix :=
[ [ 1, 8, 6, 2, 9, 4, 3, 7, 5, 19, 21, 20, 25, 27, 26, 22, 24, 23, 10, 13, 16, 15, 18, 12, 17, 11, 14 ], 
  [ 4, 2, 9, 5, 3, 7, 6, 1, 8, 22, 24, 23, 19, 21, 20, 25, 27, 26, 12, 15, 18, 14, 17, 11, 16, 10, 13 ], 
  [ 7, 5, 3, 8, 6, 1, 9, 4, 2, 25, 27, 26, 22, 24, 23, 19, 21, 20, 11, 14, 17, 13, 16, 10, 18, 12, 15 ], 
  [ 6, 1, 8, 4, 2, 9, 5, 3, 7, 24, 23, 22, 21, 20, 19, 27, 26, 25, 16, 10, 13, 12, 15, 18, 14, 17, 11 ], 
  [ 9, 4, 2, 7, 5, 3, 8, 6, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 12, 15, 11, 14, 17, 13, 16, 10 ], 
  [ 3, 7, 5, 1, 8, 6, 2, 9, 4, 21, 20, 19, 27, 26, 25, 24, 23, 22, 17, 11, 14, 10, 13, 16, 15, 18, 12 ], 
  [ 8, 6, 1, 9, 4, 2, 7, 5, 3, 26, 25, 27, 23, 22, 24, 20, 19, 21, 13, 16, 10, 18, 12, 15, 11, 14, 17 ], 
  [ 2, 9, 4, 3, 7, 5, 1, 8, 6, 20, 19, 21, 26, 25, 27, 23, 22, 24, 15, 18, 12, 17, 11, 14, 10, 13, 16 ], 
  [ 5, 3, 7, 6, 1, 8, 4, 2, 9, 23, 22, 24, 20, 19, 21, 26, 25, 27, 14, 17, 11, 16, 10, 13, 12, 15, 18 ], 
  [ 19, 22, 25, 24, 27, 21, 26, 20, 23, 10, 17, 15, 11, 18, 13, 12, 16, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5 ], 
  [ 21, 24, 27, 23, 26, 20, 25, 19, 22, 13, 11, 18, 14, 12, 16, 15, 10, 17, 4, 6, 5, 1, 3, 2, 7, 9, 8 ], 
  [ 20, 23, 26, 22, 25, 19, 27, 21, 24, 16, 14, 12, 17, 15, 10, 18, 13, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2 ], 
  [ 25, 19, 22, 21, 24, 27, 23, 26, 20, 15, 10, 17, 13, 11, 18, 14, 12, 16, 6, 5, 4, 3, 2, 1, 9, 8, 7 ], 
  [ 27, 21, 24, 20, 23, 26, 22, 25, 19, 18, 13, 11, 16, 14, 12, 17, 15, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], 
  [ 26, 20, 23, 19, 22, 25, 24, 27, 21, 12, 16, 14, 10, 17, 15, 11, 18, 13, 3, 2, 1, 9, 8, 7, 6, 5, 4 ], 
  [ 22, 25, 19, 27, 21, 24, 20, 23, 26, 17, 15, 10, 18, 13, 11, 16, 14, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3 ], 
  [ 24, 27, 21, 26, 20, 23, 19, 22, 25, 11, 18, 13, 12, 16, 14, 10, 17, 15, 2, 1, 3, 8, 7, 9, 5, 4, 6 ], 
  [ 23, 26, 20, 25, 19, 22, 21, 24, 27, 14, 12, 16, 15, 10, 17, 13, 11, 18, 5, 4, 6, 2, 1, 3, 8, 7, 9 ], 
  [ 10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 4, 7, 6, 9, 3, 8, 2, 5, 19, 26, 24, 20, 27, 22, 21, 25, 23 ], 
  [ 13, 15, 14, 10, 12, 11, 16, 18, 17, 3, 6, 9, 5, 8, 2, 7, 1, 4, 22, 20, 27, 23, 21, 25, 24, 19, 26 ], 
  [ 16, 18, 17, 13, 15, 14, 10, 12, 11, 2, 5, 8, 4, 7, 1, 9, 3, 6, 25, 23, 21, 26, 24, 19, 27, 22, 20 ], 
  [ 15, 14, 13, 12, 11, 10, 18, 17, 16, 7, 1, 4, 3, 6, 9, 5, 8, 2, 24, 19, 26, 22, 20, 27, 23, 21, 25 ], 
  [ 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 3, 6, 2, 5, 8, 4, 7, 1, 27, 22, 20, 25, 23, 21, 26, 24, 19 ], 
  [ 12, 11, 10, 18, 17, 16, 15, 14, 13, 8, 2, 5, 1, 4, 7, 6, 9, 3, 21, 25, 23, 19, 26, 24, 20, 27, 22 ], 
  [ 17, 16, 18, 14, 13, 15, 11, 10, 12, 4, 7, 1, 9, 3, 6, 2, 5, 8, 26, 24, 19, 27, 22, 20, 25, 23, 21 ], 
  [ 11, 10, 12, 17, 16, 18, 14, 13, 15, 6, 9, 3, 8, 2, 5, 1, 4, 7, 20, 27, 22, 21, 25, 23, 19, 26, 24 ], 
  [ 14, 13, 15, 11, 10, 12, 17, 16, 18, 5, 8, 2, 7, 1, 4, 3, 6, 9, 23, 21, 25, 24, 19, 26, 22, 20, 27 ] ]);
QUANDLES[27].implemented := 60;
QUANDLES[27].rack[60] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 9, 8, 7, 5, 4, 6, 23, 22, 24, 19, 21, 20, 25, 27, 26, 16, 18, 17, 14, 13, 15, 11, 10, 12 ], 
  [ 3, 2, 1, 8, 7, 9, 4, 6, 5, 22, 24, 23, 21, 20, 19, 27, 26, 25, 18, 17, 16, 13, 15, 14, 10, 12, 11 ], 
  [ 2, 1, 3, 7, 9, 8, 6, 5, 4, 24, 23, 22, 20, 19, 21, 26, 25, 27, 17, 16, 18, 15, 14, 13, 12, 11, 10 ], 
  [ 9, 8, 7, 4, 6, 5, 1, 3, 2, 21, 20, 19, 26, 25, 27, 22, 24, 23, 13, 15, 14, 12, 11, 10, 18, 17, 16 ], 
  [ 8, 7, 9, 6, 5, 4, 3, 2, 1, 20, 19, 21, 25, 27, 26, 24, 23, 22, 15, 14, 13, 11, 10, 12, 17, 16, 18 ], 
  [ 7, 9, 8, 5, 4, 6, 2, 1, 3, 19, 21, 20, 27, 26, 25, 23, 22, 24, 14, 13, 15, 10, 12, 11, 16, 18, 17 ], 
  [ 5, 4, 6, 1, 3, 2, 7, 9, 8, 26, 25, 27, 24, 23, 22, 21, 20, 19, 12, 11, 10, 17, 16, 18, 13, 15, 14 ], 
  [ 4, 6, 5, 3, 2, 1, 9, 8, 7, 25, 27, 26, 23, 22, 24, 20, 19, 21, 11, 10, 12, 16, 18, 17, 15, 14, 13 ], 
  [ 6, 5, 4, 2, 1, 3, 8, 7, 9, 27, 26, 25, 22, 24, 23, 19, 21, 20, 10, 12, 11, 18, 17, 16, 14, 13, 15 ], 
  [ 27, 26, 25, 22, 24, 23, 19, 21, 20, 10, 12, 11, 18, 17, 16, 14, 13, 15, 4, 6, 5, 3, 2, 1, 9, 8, 7 ], 
  [ 26, 25, 27, 24, 23, 22, 21, 20, 19, 12, 11, 10, 17, 16, 18, 13, 15, 14, 6, 5, 4, 2, 1, 3, 8, 7, 9 ], 
  [ 25, 27, 26, 23, 22, 24, 20, 19, 21, 11, 10, 12, 16, 18, 17, 15, 14, 13, 5, 4, 6, 1, 3, 2, 7, 9, 8 ], 
  [ 24, 23, 22, 20, 19, 21, 26, 25, 27, 18, 17, 16, 13, 15, 14, 10, 12, 11, 2, 1, 3, 7, 9, 8, 6, 5, 4 ], 
  [ 23, 22, 24, 19, 21, 20, 25, 27, 26, 17, 16, 18, 15, 14, 13, 12, 11, 10, 1, 3, 2, 9, 8, 7, 5, 4, 6 ], 
  [ 22, 24, 23, 21, 20, 19, 27, 26, 25, 16, 18, 17, 14, 13, 15, 11, 10, 12, 3, 2, 1, 8, 7, 9, 4, 6, 5 ], 
  [ 20, 19, 21, 25, 27, 26, 24, 23, 22, 14, 13, 15, 10, 12, 11, 16, 18, 17, 7, 9, 8, 5, 4, 6, 2, 1, 3 ], 
  [ 19, 21, 20, 27, 26, 25, 23, 22, 24, 13, 15, 14, 12, 11, 10, 18, 17, 16, 9, 8, 7, 4, 6, 5, 1, 3, 2 ], 
  [ 21, 20, 19, 26, 25, 27, 22, 24, 23, 15, 14, 13, 11, 10, 12, 17, 16, 18, 8, 7, 9, 6, 5, 4, 3, 2, 1 ], 
  [ 15, 14, 13, 11, 10, 12, 17, 16, 18, 8, 7, 9, 6, 5, 4, 3, 2, 1, 19, 21, 20, 27, 26, 25, 23, 22, 24 ], 
  [ 14, 13, 15, 10, 12, 11, 16, 18, 17, 7, 9, 8, 5, 4, 6, 2, 1, 3, 21, 20, 19, 26, 25, 27, 22, 24, 23 ], 
  [ 13, 15, 14, 12, 11, 10, 18, 17, 16, 9, 8, 7, 4, 6, 5, 1, 3, 2, 20, 19, 21, 25, 27, 26, 24, 23, 22 ], 
  [ 10, 12, 11, 18, 17, 16, 14, 13, 15, 5, 4, 6, 1, 3, 2, 7, 9, 8, 27, 26, 25, 22, 24, 23, 19, 21, 20 ], 
  [ 12, 11, 10, 17, 16, 18, 13, 15, 14, 4, 6, 5, 3, 2, 1, 9, 8, 7, 26, 25, 27, 24, 23, 22, 21, 20, 19 ], 
  [ 11, 10, 12, 16, 18, 17, 15, 14, 13, 6, 5, 4, 2, 1, 3, 8, 7, 9, 25, 27, 26, 23, 22, 24, 20, 19, 21 ], 
  [ 18, 17, 16, 13, 15, 14, 10, 12, 11, 1, 3, 2, 9, 8, 7, 5, 4, 6, 23, 22, 24, 19, 21, 20, 25, 27, 26 ], 
  [ 17, 16, 18, 15, 14, 13, 12, 11, 10, 3, 2, 1, 8, 7, 9, 4, 6, 5, 22, 24, 23, 21, 20, 19, 27, 26, 25 ], 
  [ 16, 18, 17, 14, 13, 15, 11, 10, 12, 2, 1, 3, 7, 9, 8, 6, 5, 4, 24, 23, 22, 20, 19, 21, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 61;
QUANDLES[27].rack[61] := rec( size := 27, matrix :=
[ [ 1, 3, 2, 8, 7, 9, 6, 5, 4, 27, 26, 25, 24, 23, 22, 20, 19, 21, 15, 14, 13, 10, 12, 11, 18, 17, 16 ], 
  [ 3, 2, 1, 7, 9, 8, 5, 4, 6, 26, 25, 27, 23, 22, 24, 19, 21, 20, 14, 13, 15, 12, 11, 10, 17, 16, 18 ], 
  [ 2, 1, 3, 9, 8, 7, 4, 6, 5, 25, 27, 26, 22, 24, 23, 21, 20, 19, 13, 15, 14, 11, 10, 12, 16, 18, 17 ], 
  [ 7, 9, 8, 4, 6, 5, 3, 2, 1, 22, 24, 23, 20, 19, 21, 25, 27, 26, 11, 10, 12, 18, 17, 16, 13, 15, 14 ], 
  [ 9, 8, 7, 6, 5, 4, 2, 1, 3, 24, 23, 22, 19, 21, 20, 27, 26, 25, 10, 12, 11, 17, 16, 18, 15, 14, 13 ], 
  [ 8, 7, 9, 5, 4, 6, 1, 3, 2, 23, 22, 24, 21, 20, 19, 26, 25, 27, 12, 11, 10, 16, 18, 17, 14, 13, 15 ], 
  [ 4, 6, 5, 2, 1, 3, 7, 9, 8, 19, 21, 20, 26, 25, 27, 24, 23, 22, 17, 16, 18, 14, 13, 15, 10, 12, 11 ], 
  [ 6, 5, 4, 1, 3, 2, 9, 8, 7, 21, 20, 19, 25, 27, 26, 23, 22, 24, 16, 18, 17, 13, 15, 14, 12, 11, 10 ], 
  [ 5, 4, 6, 3, 2, 1, 8, 7, 9, 20, 19, 21, 27, 26, 25, 22, 24, 23, 18, 17, 16, 15, 14, 13, 11, 10, 12 ], 
  [ 23, 22, 24, 21, 20, 19, 26, 25, 27, 10, 12, 11, 17, 16, 18, 15, 14, 13, 8, 7, 9, 5, 4, 6, 1, 3, 2 ], 
  [ 22, 24, 23, 20, 19, 21, 25, 27, 26, 12, 11, 10, 16, 18, 17, 14, 13, 15, 7, 9, 8, 4, 6, 5, 3, 2, 1 ], 
  [ 24, 23, 22, 19, 21, 20, 27, 26, 25, 11, 10, 12, 18, 17, 16, 13, 15, 14, 9, 8, 7, 6, 5, 4, 2, 1, 3 ], 
  [ 19, 21, 20, 26, 25, 27, 24, 23, 22, 16, 18, 17, 13, 15, 14, 12, 11, 10, 6, 5, 4, 1, 3, 2, 9, 8, 7 ], 
  [ 21, 20, 19, 25, 27, 26, 23, 22, 24, 18, 17, 16, 15, 14, 13, 11, 10, 12, 5, 4, 6, 3, 2, 1, 8, 7, 9 ], 
  [ 20, 19, 21, 27, 26, 25, 22, 24, 23, 17, 16, 18, 14, 13, 15, 10, 12, 11, 4, 6, 5, 2, 1, 3, 7, 9, 8 ], 
  [ 25, 27, 26, 22, 24, 23, 21, 20, 19, 13, 15, 14, 11, 10, 12, 16, 18, 17, 3, 2, 1, 7, 9, 8, 5, 4, 6 ], 
  [ 27, 26, 25, 24, 23, 22, 20, 19, 21, 15, 14, 13, 10, 12, 11, 18, 17, 16, 2, 1, 3, 9, 8, 7, 4, 6, 5 ], 
  [ 26, 25, 27, 23, 22, 24, 19, 21, 20, 14, 13, 15, 12, 11, 10, 17, 16, 18, 1, 3, 2, 8, 7, 9, 6, 5, 4 ], 
  [ 16, 18, 17, 13, 15, 14, 12, 11, 10, 4, 6, 5, 2, 1, 3, 7, 9, 8, 19, 21, 20, 26, 25, 27, 24, 23, 22 ], 
  [ 18, 17, 16, 15, 14, 13, 11, 10, 12, 6, 5, 4, 1, 3, 2, 9, 8, 7, 21, 20, 19, 25, 27, 26, 23, 22, 24 ], 
  [ 17, 16, 18, 14, 13, 15, 10, 12, 11, 5, 4, 6, 3, 2, 1, 8, 7, 9, 20, 19, 21, 27, 26, 25, 22, 24, 23 ], 
  [ 14, 13, 15, 12, 11, 10, 17, 16, 18, 3, 2, 1, 7, 9, 8, 5, 4, 6, 25, 27, 26, 22, 24, 23, 21, 20, 19 ], 
  [ 13, 15, 14, 11, 10, 12, 16, 18, 17, 2, 1, 3, 9, 8, 7, 4, 6, 5, 27, 26, 25, 24, 23, 22, 20, 19, 21 ], 
  [ 15, 14, 13, 10, 12, 11, 18, 17, 16, 1, 3, 2, 8, 7, 9, 6, 5, 4, 26, 25, 27, 23, 22, 24, 19, 21, 20 ], 
  [ 11, 10, 12, 18, 17, 16, 13, 15, 14, 9, 8, 7, 6, 5, 4, 2, 1, 3, 22, 24, 23, 20, 19, 21, 25, 27, 26 ], 
  [ 10, 12, 11, 17, 16, 18, 15, 14, 13, 8, 7, 9, 5, 4, 6, 1, 3, 2, 24, 23, 22, 19, 21, 20, 27, 26, 25 ], 
  [ 12, 11, 10, 16, 18, 17, 14, 13, 15, 7, 9, 8, 4, 6, 5, 3, 2, 1, 23, 22, 24, 21, 20, 19, 26, 25, 27 ] ]);
QUANDLES[27].implemented := 62;
QUANDLES[27].rack[62] := rec( size := 27, matrix :=
[ [ 1, 22, 16, 2, 23, 17, 3, 24, 18, 4, 25, 10, 5, 26, 11, 6, 27, 12, 7, 19, 13, 8, 20, 14, 9, 21, 15 ], 
  [ 17, 2, 23, 18, 3, 24, 16, 1, 22, 11, 5, 26, 12, 6, 27, 10, 4, 25, 14, 8, 20, 15, 9, 21, 13, 7, 19 ], 
  [ 24, 18, 3, 22, 16, 1, 23, 17, 2, 27, 12, 6, 25, 10, 4, 26, 11, 5, 21, 15, 9, 19, 13, 7, 20, 14, 8 ], 
  [ 6, 27, 12, 4, 25, 10, 5, 26, 11, 9, 21, 15, 7, 19, 13, 8, 20, 14, 3, 24, 18, 1, 22, 16, 2, 23, 17 ], 
  [ 10, 4, 25, 11, 5, 26, 12, 6, 27, 13, 7, 19, 14, 8, 20, 15, 9, 21, 16, 1, 22, 17, 2, 23, 18, 3, 24 ], 
  [ 26, 11, 5, 27, 12, 6, 25, 10, 4, 20, 14, 8, 21, 15, 9, 19, 13, 7, 23, 17, 2, 24, 18, 3, 22, 16, 1 ], 
  [ 8, 20, 14, 9, 21, 15, 7, 19, 13, 2, 23, 17, 3, 24, 18, 1, 22, 16, 5, 26, 11, 6, 27, 12, 4, 25, 10 ], 
  [ 15, 9, 21, 13, 7, 19, 14, 8, 20, 18, 3, 24, 16, 1, 22, 17, 2, 23, 12, 6, 27, 10, 4, 25, 11, 5, 26 ], 
  [ 19, 13, 7, 20, 14, 8, 21, 15, 9, 22, 16, 1, 23, 17, 2, 24, 18, 3, 25, 10, 4, 26, 11, 5, 27, 12, 6 ], 
  [ 16, 1, 22, 17, 2, 23, 18, 3, 24, 10, 4, 25, 11, 5, 26, 12, 6, 27, 13, 7, 19, 14, 8, 20, 15, 9, 21 ], 
  [ 23, 17, 2, 24, 18, 3, 22, 16, 1, 26, 11, 5, 27, 12, 6, 25, 10, 4, 20, 14, 8, 21, 15, 9, 19, 13, 7 ], 
  [ 3, 24, 18, 1, 22, 16, 2, 23, 17, 6, 27, 12, 4, 25, 10, 5, 26, 11, 9, 21, 15, 7, 19, 13, 8, 20, 14 ], 
  [ 12, 6, 27, 10, 4, 25, 11, 5, 26, 15, 9, 21, 13, 7, 19, 14, 8, 20, 18, 3, 24, 16, 1, 22, 17, 2, 23 ], 
  [ 25, 10, 4, 26, 11, 5, 27, 12, 6, 19, 13, 7, 20, 14, 8, 21, 15, 9, 22, 16, 1, 23, 17, 2, 24, 18, 3 ], 
  [ 5, 26, 11, 6, 27, 12, 4, 25, 10, 8, 20, 14, 9, 21, 15, 7, 19, 13, 2, 23, 17, 3, 24, 18, 1, 22, 16 ], 
  [ 14, 8, 20, 15, 9, 21, 13, 7, 19, 17, 2, 23, 18, 3, 24, 16, 1, 22, 11, 5, 26, 12, 6, 27, 10, 4, 25 ], 
  [ 21, 15, 9, 19, 13, 7, 20, 14, 8, 24, 18, 3, 22, 16, 1, 23, 17, 2, 27, 12, 6, 25, 10, 4, 26, 11, 5 ], 
  [ 7, 19, 13, 8, 20, 14, 9, 21, 15, 1, 22, 16, 2, 23, 17, 3, 24, 18, 4, 25, 10, 5, 26, 11, 6, 27, 12 ], 
  [ 22, 16, 1, 23, 17, 2, 24, 18, 3, 25, 10, 4, 26, 11, 5, 27, 12, 6, 19, 13, 7, 20, 14, 8, 21, 15, 9 ], 
  [ 2, 23, 17, 3, 24, 18, 1, 22, 16, 5, 26, 11, 6, 27, 12, 4, 25, 10, 8, 20, 14, 9, 21, 15, 7, 19, 13 ], 
  [ 18, 3, 24, 16, 1, 22, 17, 2, 23, 12, 6, 27, 10, 4, 25, 11, 5, 26, 15, 9, 21, 13, 7, 19, 14, 8, 20 ], 
  [ 27, 12, 6, 25, 10, 4, 26, 11, 5, 21, 15, 9, 19, 13, 7, 20, 14, 8, 24, 18, 3, 22, 16, 1, 23, 17, 2 ], 
  [ 4, 25, 10, 5, 26, 11, 6, 27, 12, 7, 19, 13, 8, 20, 14, 9, 21, 15, 1, 22, 16, 2, 23, 17, 3, 24, 18 ], 
  [ 11, 5, 26, 12, 6, 27, 10, 4, 25, 14, 8, 20, 15, 9, 21, 13, 7, 19, 17, 2, 23, 18, 3, 24, 16, 1, 22 ], 
  [ 20, 14, 8, 21, 15, 9, 19, 13, 7, 23, 17, 2, 24, 18, 3, 22, 16, 1, 26, 11, 5, 27, 12, 6, 25, 10, 4 ], 
  [ 9, 21, 15, 7, 19, 13, 8, 20, 14, 3, 24, 18, 1, 22, 16, 2, 23, 17, 6, 27, 12, 4, 25, 10, 5, 26, 11 ], 
  [ 13, 7, 19, 14, 8, 20, 15, 9, 21, 16, 1, 22, 17, 2, 23, 18, 3, 24, 10, 4, 25, 11, 5, 26, 12, 6, 27 ] ]);
QUANDLES[27].implemented := 63;
QUANDLES[27].rack[63] := rec( size := 27, matrix :=
[ [ 1, 26, 15, 14, 3, 25, 27, 13, 2, 24, 10, 8, 7, 23, 12, 11, 9, 22, 17, 6, 19, 21, 16, 5, 4, 20, 18 ], 
  [ 13, 2, 27, 26, 15, 1, 3, 25, 14, 9, 22, 11, 10, 8, 24, 23, 12, 7, 20, 18, 4, 6, 19, 17, 16, 5, 21 ], 
  [ 25, 14, 3, 2, 27, 13, 15, 1, 26, 12, 7, 23, 22, 11, 9, 8, 24, 10, 5, 21, 16, 18, 4, 20, 19, 17, 6 ], 
  [ 21, 16, 5, 4, 20, 18, 17, 6, 19, 14, 3, 25, 27, 13, 2, 1, 26, 15, 7, 23, 12, 11, 9, 22, 24, 10, 8 ], 
  [ 6, 19, 17, 16, 5, 21, 20, 18, 4, 26, 15, 1, 3, 25, 14, 13, 2, 27, 10, 8, 24, 23, 12, 7, 9, 22, 11 ], 
  [ 18, 4, 20, 19, 17, 6, 5, 21, 16, 2, 27, 13, 15, 1, 26, 25, 14, 3, 22, 11, 9, 8, 24, 10, 12, 7, 23 ], 
  [ 11, 9, 22, 24, 10, 8, 7, 23, 12, 4, 20, 18, 17, 6, 19, 21, 16, 5, 27, 13, 2, 1, 26, 15, 14, 3, 25 ], 
  [ 23, 12, 7, 9, 22, 11, 10, 8, 24, 16, 5, 21, 20, 18, 4, 6, 19, 17, 3, 25, 14, 13, 2, 27, 26, 15, 1 ], 
  [ 8, 24, 10, 12, 7, 23, 22, 11, 9, 19, 17, 6, 5, 21, 16, 18, 4, 20, 15, 1, 26, 25, 14, 3, 2, 27, 13 ], 
  [ 26, 15, 1, 3, 25, 14, 13, 2, 27, 10, 8, 24, 23, 12, 7, 9, 22, 11, 6, 19, 17, 16, 5, 21, 20, 18, 4 ], 
  [ 2, 27, 13, 15, 1, 26, 25, 14, 3, 22, 11, 9, 8, 24, 10, 12, 7, 23, 18, 4, 20, 19, 17, 6, 5, 21, 16 ], 
  [ 14, 3, 25, 27, 13, 2, 1, 26, 15, 7, 23, 12, 11, 9, 22, 24, 10, 8, 21, 16, 5, 4, 20, 18, 17, 6, 19 ], 
  [ 16, 5, 21, 20, 18, 4, 6, 19, 17, 3, 25, 14, 13, 2, 27, 26, 15, 1, 23, 12, 7, 9, 22, 11, 10, 8, 24 ], 
  [ 19, 17, 6, 5, 21, 16, 18, 4, 20, 15, 1, 26, 25, 14, 3, 2, 27, 13, 8, 24, 10, 12, 7, 23, 22, 11, 9 ], 
  [ 4, 20, 18, 17, 6, 19, 21, 16, 5, 27, 13, 2, 1, 26, 15, 14, 3, 25, 11, 9, 22, 24, 10, 8, 7, 23, 12 ], 
  [ 9, 22, 11, 10, 8, 24, 23, 12, 7, 20, 18, 4, 6, 19, 17, 16, 5, 21, 13, 2, 27, 26, 15, 1, 3, 25, 14 ], 
  [ 12, 7, 23, 22, 11, 9, 8, 24, 10, 5, 21, 16, 18, 4, 20, 19, 17, 6, 25, 14, 3, 2, 27, 13, 15, 1, 26 ], 
  [ 24, 10, 8, 7, 23, 12, 11, 9, 22, 17, 6, 19, 21, 16, 5, 4, 20, 18, 1, 26, 15, 14, 3, 25, 27, 13, 2 ], 
  [ 15, 1, 26, 25, 14, 3, 2, 27, 13, 8, 24, 10, 12, 7, 23, 22, 11, 9, 19, 17, 6, 5, 21, 16, 18, 4, 20 ], 
  [ 27, 13, 2, 1, 26, 15, 14, 3, 25, 11, 9, 22, 24, 10, 8, 7, 23, 12, 4, 20, 18, 17, 6, 19, 21, 16, 5 ], 
  [ 3, 25, 14, 13, 2, 27, 26, 15, 1, 23, 12, 7, 9, 22, 11, 10, 8, 24, 16, 5, 21, 20, 18, 4, 6, 19, 17 ], 
  [ 5, 21, 16, 18, 4, 20, 19, 17, 6, 25, 14, 3, 2, 27, 13, 15, 1, 26, 12, 7, 23, 22, 11, 9, 8, 24, 10 ], 
  [ 17, 6, 19, 21, 16, 5, 4, 20, 18, 1, 26, 15, 14, 3, 25, 27, 13, 2, 24, 10, 8, 7, 23, 12, 11, 9, 22 ], 
  [ 20, 18, 4, 6, 19, 17, 16, 5, 21, 13, 2, 27, 26, 15, 1, 3, 25, 14, 9, 22, 11, 10, 8, 24, 23, 12, 7 ], 
  [ 22, 11, 9, 8, 24, 10, 12, 7, 23, 18, 4, 20, 19, 17, 6, 5, 21, 16, 2, 27, 13, 15, 1, 26, 25, 14, 3 ], 
  [ 7, 23, 12, 11, 9, 22, 24, 10, 8, 21, 16, 5, 4, 20, 18, 17, 6, 19, 14, 3, 25, 27, 13, 2, 1, 26, 15 ], 
  [ 10, 8, 24, 23, 12, 7, 9, 22, 11, 6, 19, 17, 16, 5, 21, 20, 18, 4, 26, 15, 1, 3, 25, 14, 13, 2, 27 ] ]);
QUANDLES[27].implemented := 64;
QUANDLES[27].rack[64] := rec( size := 27, matrix :=
[ [ 1, 13, 25, 21, 6, 18, 11, 23, 8, 26, 2, 14, 16, 19, 4, 9, 12, 24, 15, 27, 3, 5, 17, 20, 22, 7, 10 ], 
  [ 26, 2, 14, 16, 19, 4, 9, 12, 24, 15, 27, 3, 5, 17, 20, 22, 7, 10, 1, 13, 25, 21, 6, 18, 11, 23, 8 ], 
  [ 15, 27, 3, 5, 17, 20, 22, 7, 10, 1, 13, 25, 21, 6, 18, 11, 23, 8, 26, 2, 14, 16, 19, 4, 9, 12, 24 ], 
  [ 14, 26, 2, 4, 16, 19, 24, 9, 12, 3, 15, 27, 20, 5, 17, 10, 22, 7, 25, 1, 13, 18, 21, 6, 8, 11, 23 ], 
  [ 3, 15, 27, 20, 5, 17, 10, 22, 7, 25, 1, 13, 18, 21, 6, 8, 11, 23, 14, 26, 2, 4, 16, 19, 24, 9, 12 ], 
  [ 25, 1, 13, 18, 21, 6, 8, 11, 23, 14, 26, 2, 4, 16, 19, 24, 9, 12, 3, 15, 27, 20, 5, 17, 10, 22, 7 ], 
  [ 27, 3, 15, 17, 20, 5, 7, 10, 22, 13, 25, 1, 6, 18, 21, 23, 8, 11, 2, 14, 26, 19, 4, 16, 12, 24, 9 ], 
  [ 13, 25, 1, 6, 18, 21, 23, 8, 11, 2, 14, 26, 19, 4, 16, 12, 24, 9, 27, 3, 15, 17, 20, 5, 7, 10, 22 ], 
  [ 2, 14, 26, 19, 4, 16, 12, 24, 9, 27, 3, 15, 17, 20, 5, 7, 10, 22, 13, 25, 1, 6, 18, 21, 23, 8, 11 ], 
  [ 24, 9, 12, 14, 26, 2, 4, 16, 19, 10, 22, 7, 3, 15, 27, 20, 5, 17, 8, 11, 23, 25, 1, 13, 18, 21, 6 ], 
  [ 10, 22, 7, 3, 15, 27, 20, 5, 17, 8, 11, 23, 25, 1, 13, 18, 21, 6, 24, 9, 12, 14, 26, 2, 4, 16, 19 ], 
  [ 8, 11, 23, 25, 1, 13, 18, 21, 6, 24, 9, 12, 14, 26, 2, 4, 16, 19, 10, 22, 7, 3, 15, 27, 20, 5, 17 ], 
  [ 7, 10, 22, 27, 3, 15, 17, 20, 5, 23, 8, 11, 13, 25, 1, 6, 18, 21, 12, 24, 9, 2, 14, 26, 19, 4, 16 ], 
  [ 23, 8, 11, 13, 25, 1, 6, 18, 21, 12, 24, 9, 2, 14, 26, 19, 4, 16, 7, 10, 22, 27, 3, 15, 17, 20, 5 ], 
  [ 12, 24, 9, 2, 14, 26, 19, 4, 16, 7, 10, 22, 27, 3, 15, 17, 20, 5, 23, 8, 11, 13, 25, 1, 6, 18, 21 ], 
  [ 11, 23, 8, 1, 13, 25, 21, 6, 18, 9, 12, 24, 26, 2, 14, 16, 19, 4, 22, 7, 10, 15, 27, 3, 5, 17, 20 ], 
  [ 9, 12, 24, 26, 2, 14, 16, 19, 4, 22, 7, 10, 15, 27, 3, 5, 17, 20, 11, 23, 8, 1, 13, 25, 21, 6, 18 ], 
  [ 22, 7, 10, 15, 27, 3, 5, 17, 20, 11, 23, 8, 1, 13, 25, 21, 6, 18, 9, 12, 24, 26, 2, 14, 16, 19, 4 ], 
  [ 17, 20, 5, 7, 10, 22, 27, 3, 15, 6, 18, 21, 23, 8, 11, 13, 25, 1, 19, 4, 16, 12, 24, 9, 2, 14, 26 ], 
  [ 6, 18, 21, 23, 8, 11, 13, 25, 1, 19, 4, 16, 12, 24, 9, 2, 14, 26, 17, 20, 5, 7, 10, 22, 27, 3, 15 ], 
  [ 19, 4, 16, 12, 24, 9, 2, 14, 26, 17, 20, 5, 7, 10, 22, 27, 3, 15, 6, 18, 21, 23, 8, 11, 13, 25, 1 ], 
  [ 21, 6, 18, 11, 23, 8, 1, 13, 25, 16, 19, 4, 9, 12, 24, 26, 2, 14, 5, 17, 20, 22, 7, 10, 15, 27, 3 ], 
  [ 16, 19, 4, 9, 12, 24, 26, 2, 14, 5, 17, 20, 22, 7, 10, 15, 27, 3, 21, 6, 18, 11, 23, 8, 1, 13, 25 ], 
  [ 5, 17, 20, 22, 7, 10, 15, 27, 3, 21, 6, 18, 11, 23, 8, 1, 13, 25, 16, 19, 4, 9, 12, 24, 26, 2, 14 ], 
  [ 4, 16, 19, 24, 9, 12, 14, 26, 2, 20, 5, 17, 10, 22, 7, 3, 15, 27, 18, 21, 6, 8, 11, 23, 25, 1, 13 ], 
  [ 20, 5, 17, 10, 22, 7, 3, 15, 27, 18, 21, 6, 8, 11, 23, 25, 1, 13, 4, 16, 19, 24, 9, 12, 14, 26, 2 ], 
  [ 18, 21, 6, 8, 11, 23, 25, 1, 13, 4, 16, 19, 24, 9, 12, 14, 26, 2, 20, 5, 17, 10, 22, 7, 3, 15, 27 ] ]);
QUANDLES[27].implemented := 65;
QUANDLES[27].rack[65] := rec( size := 27, matrix :=
[ [ 1, 27, 14, 17, 4, 21, 24, 11, 7, 6, 20, 16, 10, 9, 23, 26, 13, 3, 8, 22, 12, 15, 2, 25, 19, 18, 5 ], 
  [ 15, 2, 25, 19, 18, 5, 8, 22, 12, 17, 4, 21, 24, 11, 7, 1, 27, 14, 10, 9, 23, 26, 13, 3, 6, 20, 16 ], 
  [ 26, 13, 3, 6, 20, 16, 10, 9, 23, 19, 18, 5, 8, 22, 12, 15, 2, 25, 24, 11, 7, 1, 27, 14, 17, 4, 21 ], 
  [ 27, 14, 1, 4, 21, 17, 11, 7, 24, 20, 16, 6, 9, 23, 10, 13, 3, 26, 22, 12, 8, 2, 25, 15, 18, 5, 19 ], 
  [ 2, 25, 15, 18, 5, 19, 22, 12, 8, 4, 21, 17, 11, 7, 24, 27, 14, 1, 9, 23, 10, 13, 3, 26, 20, 16, 6 ], 
  [ 13, 3, 26, 20, 16, 6, 9, 23, 10, 18, 5, 19, 22, 12, 8, 2, 25, 15, 11, 7, 24, 27, 14, 1, 4, 21, 17 ], 
  [ 14, 1, 27, 21, 17, 4, 7, 24, 11, 16, 6, 20, 23, 10, 9, 3, 26, 13, 12, 8, 22, 25, 15, 2, 5, 19, 18 ], 
  [ 25, 15, 2, 5, 19, 18, 12, 8, 22, 21, 17, 4, 7, 24, 11, 14, 1, 27, 23, 10, 9, 3, 26, 13, 16, 6, 20 ], 
  [ 3, 26, 13, 16, 6, 20, 23, 10, 9, 5, 19, 18, 12, 8, 22, 25, 15, 2, 7, 24, 11, 14, 1, 27, 21, 17, 4 ], 
  [ 17, 4, 21, 24, 11, 7, 1, 27, 14, 10, 9, 23, 26, 13, 3, 6, 20, 16, 15, 2, 25, 19, 18, 5, 8, 22, 12 ], 
  [ 19, 18, 5, 8, 22, 12, 15, 2, 25, 24, 11, 7, 1, 27, 14, 17, 4, 21, 26, 13, 3, 6, 20, 16, 10, 9, 23 ], 
  [ 6, 20, 16, 10, 9, 23, 26, 13, 3, 8, 22, 12, 15, 2, 25, 19, 18, 5, 1, 27, 14, 17, 4, 21, 24, 11, 7 ], 
  [ 4, 21, 17, 11, 7, 24, 27, 14, 1, 9, 23, 10, 13, 3, 26, 20, 16, 6, 2, 25, 15, 18, 5, 19, 22, 12, 8 ], 
  [ 18, 5, 19, 22, 12, 8, 2, 25, 15, 11, 7, 24, 27, 14, 1, 4, 21, 17, 13, 3, 26, 20, 16, 6, 9, 23, 10 ], 
  [ 20, 16, 6, 9, 23, 10, 13, 3, 26, 22, 12, 8, 2, 25, 15, 18, 5, 19, 27, 14, 1, 4, 21, 17, 11, 7, 24 ], 
  [ 21, 17, 4, 7, 24, 11, 14, 1, 27, 23, 10, 9, 3, 26, 13, 16, 6, 20, 25, 15, 2, 5, 19, 18, 12, 8, 22 ], 
  [ 5, 19, 18, 12, 8, 22, 25, 15, 2, 7, 24, 11, 14, 1, 27, 21, 17, 4, 3, 26, 13, 16, 6, 20, 23, 10, 9 ], 
  [ 16, 6, 20, 23, 10, 9, 3, 26, 13, 12, 8, 22, 25, 15, 2, 5, 19, 18, 14, 1, 27, 21, 17, 4, 7, 24, 11 ], 
  [ 24, 11, 7, 1, 27, 14, 17, 4, 21, 26, 13, 3, 6, 20, 16, 10, 9, 23, 19, 18, 5, 8, 22, 12, 15, 2, 25 ], 
  [ 8, 22, 12, 15, 2, 25, 19, 18, 5, 1, 27, 14, 17, 4, 21, 24, 11, 7, 6, 20, 16, 10, 9, 23, 26, 13, 3 ], 
  [ 10, 9, 23, 26, 13, 3, 6, 20, 16, 15, 2, 25, 19, 18, 5, 8, 22, 12, 17, 4, 21, 24, 11, 7, 1, 27, 14 ], 
  [ 11, 7, 24, 27, 14, 1, 4, 21, 17, 13, 3, 26, 20, 16, 6, 9, 23, 10, 18, 5, 19, 22, 12, 8, 2, 25, 15 ], 
  [ 22, 12, 8, 2, 25, 15, 18, 5, 19, 27, 14, 1, 4, 21, 17, 11, 7, 24, 20, 16, 6, 9, 23, 10, 13, 3, 26 ], 
  [ 9, 23, 10, 13, 3, 26, 20, 16, 6, 2, 25, 15, 18, 5, 19, 22, 12, 8, 4, 21, 17, 11, 7, 24, 27, 14, 1 ], 
  [ 7, 24, 11, 14, 1, 27, 21, 17, 4, 3, 26, 13, 16, 6, 20, 23, 10, 9, 5, 19, 18, 12, 8, 22, 25, 15, 2 ], 
  [ 12, 8, 22, 25, 15, 2, 5, 19, 18, 14, 1, 27, 21, 17, 4, 7, 24, 11, 16, 6, 20, 23, 10, 9, 3, 26, 13 ], 
  [ 23, 10, 9, 3, 26, 13, 16, 6, 20, 25, 15, 2, 5, 19, 18, 12, 8, 22, 21, 17, 4, 7, 24, 11, 14, 1, 27 ] ]);


